Have you checked out the recent threads here about this exact topic?
A compass plane would probably work, but the grain would almost
certainly be going different directions on each side of the convex
curve. Therefore you could plane with the grain "downhill" on each
side, but you'll still have to do some sanding/scraping in the middle
where the grain direction changes.
My advice: spend some quality time tuning your bandsaw to reduce
vibration to get smoother cuts to start with. If you don't have a
bandsaw book (i.e. Mark Duginske or others), get one. Tuning/tweaking
might take a while, but it should pay off during this project alone if
it reduces sanding on 12+ curved chair rails. Your new blade guides
certainly won't hurt either.
Also, if you weren't already planning on it, cut the tenons on your
stock before you cut the curves.
Good luck,
Andy