How common is the 19.5" tire, i.e. how long will you have to drive on the spare?
If you are using the spare as a get me off the road to the nearest tire store or campground, then a different spare should not be a problem with a couple of caveats. On the front will pose steering issues, on the rear it could cause problems with the limited slip. In newer trucks it would also effect sway control and the other automated safety systems.
In this regard, the stock spare should work with a little extra effort of mounting the spare on the front and then moving the front 19.5" to the rear.
If you want to continue on your way at highway speeds, the tires should be the same size or it will create steering, handling, and limited slip issues.