They had loafers and scalawags back then too; I would have been just fine.
There were government statisticians in 1954, so I could have been doing the same work then. But Lord, would it ever be painful to do without computing tools from the 1980s or later.
OTOH, the ratio of math PhDs to full-time college professor positions was quite favorable in the mid-1950s, so I could have been doing that instead. And I could have been a college professor in 1904 as well, when government statisticians didn’t exist for all practical purposes.
Could have been doing that in 1904, but probably wouldn’t have had the patience to pass the series of exams in 1954. Also, I don’t know how much writing an actuary has to do to explain how he came up with his risk assessments (I’d guess it would be a nontrivial part of the job), but I wouldn’t have wanted any career involving much writing before the age of personal word processing. It would feel like having an arm amputated.
In 1954 I’d probably still be a statistician, possibly and actuary. In 1904 I’d probably be a college professor in mathematics.
Same. In fact, I have on occasion cited cases from before 1904 - and I know you have, too.
Remember this game? 
http://boards.straightdope.com/sdmb/showthread.php?t=705567&highlight="code+justinian"
2014: Commercial insurance broker specializing in shipping & logistics companies.
1954: Ditto
1904: Ditto
That’s boring.
Same job I have now but type- or hand-writing everything.
Electrical engineer. Probably could be doing that job in 1954 and 1904.
However, I mostly do programming for “Smart Grid” applications so my exact work would be different in those years. Still, I like to think I know enough about power systems to have scraped by 110 years ago. In 1904 I could have been a Tesla contemporary, cleaning up after the War of the Currents. Exciting time.
Carpenter. That was my original intent before getting into electronics and computers.
1904 would be a challenge. All hand tools. No plywood sheeting. A lot more work and carpenters back then were more skilled. It would be quite a shock to go back to that time. Heck they still used square nails. 
Carpenters today have different skills. They have to know all the code requirements. Insulation, vapor barrier and attic venting are very important. You get mold if its done wrong. Carpentry today is more technical.