Thank you. Sorry to seem obtuse.
Believe it or not I put “steel puddler” into wiki’s search box; it seems I didn’t scroll down far enough to see the word puddling. One more proof that a man has got to be smarter than his tools. Which I wasn’t.
There’s some weirdos out there who shoot old flintlocks, like me. There are lots of places that sell us flints that were hand-knapped, by professional flint knappers.
Proof Operators are alive and well and make about $12/hour on average. There is really no automated way to encode the dollar amount on the MICR line of a check other than a proof machine. Even though some ATM’s and bank apps have optical scanners that “read” the check and decipher the amount, they are not yet reliable enough not fast enough to replace a human.
It wasn’t always to the detriment of heavy metal bands.
My aunt started work as a keypunch operator at the state capitol in the 1970s. She was there until she retired, and went through all of the various upgrades, learning every new system as it was introduced.
I don’t believe there are any stokers.
Plague doctors. I’m pretty sure there are no more plague doctors.
There are still scribes though. In Judaism, they’re called “sofers,” and make hand copies of the Torah, and an few other handwritten documents (like mezzuzah scrolls) for Judaism.
ETA: No more castrati-- at least, the ones made for Catholic church choirs.
I’m surprised nobody else has mentioned this one.
Then again, perhaps someone is still making money at it:
Daily Herald
Yeah, as in “New York Daily Herald” and various other newspapers which took their names from the age-old job*. A herald (or harold) was a guy who shouted really loud – announcing the entrance of important people and telling people the news, originally of the court and the royal business. Later, heralds and cryers (not a professionally despondent tear-leaker) were the ones who worked for newspapers and shouted out the headlines – “…read all about it!” to sell newspapers in the street. And slowly the newspapers went to delivery boys and news stands and the heralds were phased out. I still see people selling newspapers in the middle of intersections, but they just stand there and wait for someone who’s waiting to make a left hand turn at the light to roll down their window and fork over some money.
—G!
It’s also interesting to note that many family names are basically professions used as surnames – sawyer, cooper, ____wright (or just “Wright” alone), farmer, potter, smith, et cetera.
I am not sure how few you think would make something “niche/artisanal,” but farriers are a solid trade with thousands of practitioners. (25,000 in the U.S. according to this site.) In contrast, there were just over 4700 heart surgeons (with declining numbers) in 2005 according to this trade journal report.
Wrought iron workers are probably quite a bit fewer, only 4,000 according to Wikipedia, but the word blacksmith evokes the image of a farrier more than that of a decorative iron worker.
Are farriers as common as they were in 1900? Certainly not. However, as long as people continue to employ horses for racing–thoroughbred & harness, hunters, jumpers, dressage, western, the various specialty gaited breeds, farming, (lots of Amish in PA, OH, KY, IN, MN and other locations), ranching, and simple pleasure ownership, there will be a need for farriers.
I suspect that with over 130 racetracks, (and a lot of wealthy horse owners), grooms may be more prevalent than one would first guess, as well.
I did that during my “Gap Year”, which I took 30 years before it had a name. Several years later, I returned to the same company in a different department, where I was a data entry operator, and found that my old department no longer existed; the employees all transferred to other jobs, whether in or out of the company, and in time a couple of my old coworkers came to work there too.
When a person does data entry, the data goes directly into the computer. When a person does (did) keypunch, the data had to be transcribed onto magnetic tape, punch cards, and who knows what else, which was then fed into the computer. The punch card machine was there when I started in 1981 and phased out less than a year later.
I used to live in an area with a large Amish population. Someone has to make those buggies.
One of the area’s biggest employers was a company that made wine and whiskey barrels; the wood was harvested and milled elsewhere, and you could always tell when they got a shipment because you could smell the fresh wood while driving on the Interstate a few blocks away. Defective barrels were available for sale to the public, usually sawed in half, and the downtown trash cans were modified from some of these barrels. 
I’ve been wondering for a few years now whether there are still any operational Linotype/Monotype machines anywhere in the world. So that raises the question, for this thread, whether any Linotype Operators are still working.
See Tables 1 and 3 in that article. There are many fewer horses in the U.S. than there used to be; the high point was a century ago. Think of all the livery stables in cities and towns across the country that don’t exist anymore - no jobs for grooms there.
Not to mention that buggy whips and riding crops have other uses than the intended ones by people with certain inclinations. Ahem.
Tinker.
's dammer.
And got a TV series out of it.
I think the distinction is between people who keep the old knowledge alive alongside something else that is more likely their primary business, and those who are able to make a living out of only the old knowledge (which is probably not that many, if any).
A related career which probably disappeared, at least officially, is the strike breaker ; the guys who’d not only get called upon to bash heads in when a strike is in effect, but also bust the teeth of “uppity” workers and suspected “reds” or unionists the rest of the time.
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Plague doctors. I’m pretty sure there are no more plague doctors.
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I’m pretty sure there are still some plague specialists at the CDC just in case 
I first read that as Thinker, and was about to dejectedly agree :D.
Are there still some newspapers that employ old-timey type setters ?
How about the venerable profession of lamplighter?