It was explained to me a while ago (and for the benefit of others) that drilling through the rim joist in THIS particular case is OK because, with a rim joist, the weight is straight down and spread out very well (especially if the joist is on a foundation wall made of cement block or poured cement.)
I have a poured cement basement wall. On top of it is the rim joist. On top of that is 3/4" sub-floor. On top of THAT is the baseplate for the 1st floor wall(s). The rim joist isn't really functioning like a 'header' as a header functions. A header 'spans' a distance w/o any support. In my example, the rim joist is supported every which way but loose. (Hence, it's not a header.) With that, you should have no problem cutting through the rim joist. In fact, in my home, which is 2 years old, the vent for the how water heater and the clothes dryer are cut into the rim joist, centered. BUT, to be sure, you might want to check around. Stop by any construction site or ask a local Plumbing Supply House for 'guidance'.
Oh, one last thing, IF your ductwork runs through a cold 'space', like a crawlspace or part of your unheated basement, be sure to insulate the duct. My best to ya and hope this helps.
Jay J -Moderator
PS: Be sure your fan is OK for the b-room AND the duct's length you're using. Again, check with a Supplier in your area.