Hey Chris,
Any structure built before 1978 is assumed to have lead-based paint, according to the EPA's "RRP" (Renovate, Repair, Paint) program, so I think you can safely assume that in your 1908 home you have it.
Lead is a neurotoxin that particularly effects young children. It's also cumulative with no good way to remove it from our systems. Being careful with lead contamination in your child's room is the right thing to do.
Avoid any process that might atomize the paint or introduce lead-contaminated dust into the room. Misting the area where you are working with a water bottle helps keep dust from becoming airborne. If you have to sand, definitely use your Hepa-filtered vac to contain the dust, then repeatedly wipe down the entire area with wet Swiffers until they come up clean. Personal protection for you is important, too - use a mask that is rated for lead dust. The cheapie nuisance dust masks won't do the job. Lastly, if you create any dust, don't walk around the house after you finish working; you'll just spread the stuff all over. The best thing is to get a set of the inexpensive Tyvek coveralls and when you're done working, take them off in the room, bag them and dispose of them. Wipe down your shoes, too.
These are all procedures that are taught when you take the EPA certification course for lead safe work practices.
I guess I would try to free the paint-welded window with a utility knife or something that didn't create a lot of mess.
Overkill? Maybe. It sounds like a lot of effort, I know, but lead exposure is no joke - especially for your kids.
Good luck and be safe.