What to do about rats/squirrels in a space too small for us to access?

I've been hearing scurrying in the ceiling of my home office, which is a bump out built separately from the main house. Not sure if it was a mistake during the build or just wear and tear over the years, but husband got on the roof and found there's a small hole and that's where those fuckers are hanging out.

I feel like I'm living in a more annoying version of the tell tale heart listening to these dicks on and off all day. We could setup traps, but if they die they're going to decompose and stink up the joint if we can't get them out.

Do I need to hire someone or does anyone have creative ideas on how to fix?