I'd go with at least a 24" bbl. with the stw. If you weren't hanging that long of a can on the end I'd say to go with 26" or more.
Can you go to an 1885 or #1 action to get the overall length of the rifle down??
If you are stuck on a 20-22" bbl. length a 280AI or 7rem may be a bit better option as it'll make less noise with the can and will make use of the shorter barrel length better; you'll probably get nearly the same speed with all three cal's in a 20" bbl and the stw will be harder to get accurate as your muzzle pressure will be higher and want to kick the bullet around a bit more.
The strain gauge graph here is the win 150 grain factory load fired in my old sendero 7mmstw. Notice the secondary peak; that was a tight spot at 16" down the bore and the pressure is still at 30 Kpsi.