Usually, around here at least, making up frames after arriving a bit late is left up to a "Gentleman's agreement" type of thing where, as long as the team captains agree it is OK, the tardy bowler is allowed to make up the frames.
As for the tenth frame thing, remember Del Ballard? He needed only a few pins for a win, and stayed with his regular ball. Lost it a bit at the bottom of the swing, and watched as it fell into the channel, causing him to lost several thousand dollars and a tournament win.
If he had thrown his spare ball down the middle, he would've gotten well more than enough for the win.
So, given this, I would say that I would recommend my team mate throw whichever of the two the THEY felt the most comfortable with.
Me personally, I would prefer to throw my strike ball probably 99% of the time.