Optometry.
A lot of artistic professions. Even if you have natural talent, you need to spend years aquiring the skills. But people rarely die from a poorly executed piece of art.
The OP excluded anything having to do with education, though. Depending on the specific job a librarian could be partially or primarily an educator – I’m an academic librarian and spend a lot of time doing classroom instruction – and I’d say most librarian have at least some connection to some type of education.
I guess it depends on what the OP means by “low-risk”. One of my best friends is an opera singer by training and even has a Master’s in voice, but she has yet to land an actual paying role in an opera. (She makes money giving singing lessons.) I gather that the world of professional opera is very stressful in addition to the high rate of unemployment, so I’d consider it a fairly risky field.
ETA: Oh, my vote is also for actuary.
If I’m reading the OP correctly, s/he’s looking for professions which are low-risk for other people, not the professional. There is a lot of stress in the opera world (I know this from experience), not to mention actual physical risk from stage accidents (I once fell off a stage level while holding a sword), but the audience is more or less safe even if the performer messes up.
The OP specifies “little personal risk or risk to those served by the professional”, so that includes both risk to the professional and risk to others. But I’m not clear on whether we’re supposed to be considering risk only in terms of physical injury or also include things like stress or financial risk.
Well, you might have landed on an audience member when you fell holding that sword! 
In general, I think you have to discount at least financial risk, since screwing up in any profession carries with it a risk of firing in the case of screwing up.
That would have been quite a fall, since there was about 8 feet of stage and fifteen feet of floor between me and the audience.
I had in mind risk for both the professional and those served by the professional, but I wasn’t thinking about the risk of not being able to find a position.
The framework for this is wanting things to contrast with “schoolteacher” on a, whatddyacallit, two-axis quadrant plot where one axis is “risk” and one is “training”. A surgeon obviously risks his patients’ lives and requires lots of training, so that profession is in the “high risk, high training” quadrant. A commercial fisherman is in the “high risk, low training” quadrant, as shown on, what is that show, the Somethingest Catch. A teacher is commonly thought of as being in the “low risk, low training” quadrant, although not as far out on the axes as, say, “Walmart greeter”. The point will be made that teachers certainly benefit from more training than many of them get, and that the risk is that their students won’t learn anything; teachers might benefit from a changed perception of where they belong on the axes. Just for balance, I wanted professions to mention in the fourth quadrant and couldn’t think of any good ones offhand.
This is all for somebody else’s presentation, and I was asked to make the graphic for it on short notice. Graphic now made; presentation coming soon. Edits possible.
Papercuts! PAPERCUTS!!!
Pharmacy just popped into my head. Even though it can arguably be quite dangerous to give a person the wrong drugs, I’m not sure that pharmacists nowadays really do a lot of the stuff that they are trained to do.
The pharmacist goes and gets a doctoral degree to do what- count pills out of a factory sealed bottle? How often do pharmacists synthesize drugs on-site?
I’m not sure if you can really call teachers low-training nowadays.
Perhaps social workers? What, get a master’s degree just to exercise common sense?
“You drink too much. You should go to rehab.”
“Stop hitting your sister.”
etc.
Are you kidding? I just spent a fascinating afternoon learning about the various types of on-the-job injuries suffered by thoroughbred racehorse jockeys, exercise riders, and trainers. My favorite accident description: “Horse went down on trainer.” :eek: :eek: :eek:
Nah; been a matrimonial attorney for 6 years, and the closest I ever came to violence was with another attorney.
Pharmacists are better informed about drug interactions than pretty much anyone else out there.
You may want to look into social work training…
Jedi Knight
or
Klingon linguistics expert
I assume you’re joking a bit, but most of the pill counters are not pharmacists. The PharmD degree is pretty advanced, but I believe a bit less schooling than an MD or even PhD. A main part of their job is to make sure that their patients aren’t taking drug combinations that will kill them, all because the GP or other doctor didn’t look into it thoroughly enough.
I am also not sure what you think Social Workers do. They aren’t purely therapists, and certainly aren’t live coaches. A lot of their training does seem to be BS, but much of it isn’t. It’s not a low-stress job in many focus areas. I know people who have done similar work (like social work without the MSW degree), and you have to help kids who went through terrible abuse their entire lives. It’s very emotionally draining. Don’t know if that counts as risk per the OP, though.
Since my sister was a social worker for years, I can say I think it’s a medium-to-high-risk job per my OP: risk to social worker is despair, burnout, and crazy clients or clients’ associates; risk to those served is much higher, though. Social workers help battered women & children get out of homes where the batterer endangers their lives. Sis worked at various shelters, then as a victim’s advocate in the courts. She spent a lot of time either convincing victims to get the hell out, or convincing various service providers to pony up and provide the damn services already so the victims COULD get the hell out. Or stay the hell out.
Then there were the crazy ones. I so, so wish she’d write up some of her stories, as I would be her editor, and we’d make a spoontillion dollars. There is some quality crazy out there, lemme tell ya.
The OP states low risks to others. I would say, being in the field, that Architecture most certainly can cause a lot of damage if not done right. Stress levels can be very high, depending on where you work.
(Bolding mine.) Yeah. I was a maths major, so I shared a lot of courses with actuarial science students, and now that I’m a graduate tutor I teach a lot of them. (Seriously, more than half the students in our Maths II course are ac. sci. majors.) And they are some of the most stressed-out students on campus. They have a heavy course load, and some of the courses have ridiculously low pass rates. And then once they get the degree they still have to write board exams to qualify as an actuary!
Not to mention that, at my university, less that half of the students who initially register as ac. sci. majors actually end up graduating with that degree.
Stress I’ll give you, but anything big is gonna require a structural engineer to sign off on anyways. The architect has to make sure it’s not a hideously awkward design, but there are a whole hep of regulations in place to make sure it’s not dangerous (in the US, anyhow). Now, contractor or structural engineer, that’s a different story…
I’ll second musical repair (I know a guy who does accordion repair, and it’s pretty crazy how complicated those things are), and also watch design/repair. It’s not on the same level as law, but three years of school is a fair amount for making sure someone’s on time.
Likewise, pretty much any design field that can’t injure someone - graphic, fashion, packaging. A lot of people get Master’s, but nobody’s gonna die if you use the wrong typeface.
But the ultimate field? Mathematics. Those guys spend crazy amounts of time studying absurdly arcane stuff, but the chances of someone getting hurt… well, ask an actuary, I can’t even imagine.
Folks who specialize in this have lines out the door - e.g., luthiers who only repair pre-War Martin acoustic guitars.
But - the responsibility for restoring and repairing them - and holding the hopes of the owner/player in your hands…I suppose there’s some risk 
Obligatory xkcd link.
Although mathematics isn’t on the chart, I only found one non-xkcd use of the phrase, so you should be fairly safe.