Well, the short answer is "yes", FMP could handle this sort of thing.
> these are pretty long and specific documents, but they all follow the same format and have the same sort of variables in it.
You can set it up so that the basic text of the document remains "static" while the "variables" (like names and so on) can be set up as "Merge fields" inserted into the relevant places within the static text.
Things may get a bit more complicated, however, if, for instance, the law changes at some point in the future and you're required to issue updated "Safe Work Statements", which means the text of your document would probably need to change here and there. The design of your database may need to take that contingency into account. You may find that certain "blocks" of text would be better set up as actual fields (rather than static text), so that they can be edited, if need be.
I'd recommend that you download the trial version of FMP and play around with it for a bit. If you're computer savvy, you should be able to get things up and running fairly quickly. If you run into difficulties, you can always ask questions here.
And really, given what they're asking you to do, I reckon your employers ought to cough up for some sort of FMP training for you. I mean, they wouldn't expect you to operate, say, a forklift without training, would they? ;-)