A broken arm. Also known as a "Saiyan scratch." Goku blasted Vegeta into orbit with a broken arm.
Yeah, Vegeta took having his arm broken like a champ in canon.
Seriously, I'm pretty sure he had both arms working at this point. And even if not, every injury he took, it was during said fight against Vegeta (who wasn't exactly unscathed either after that round of Kaiokenx3), it's not as if Vegeta ambushed him when he was already down.
The way I see it, your suggestion can only end badly. If we win, we just ambushed an injured warrior, added insult to injury, and you can bet he'll be out for revenge at the first opportunity. Possibly waiting for a time when
we have a broken arm, see if we like it. If we lose, it's basically an utter humiliation, we tried to beat someone while he's down, and couldn't even manage that. The only thing we'll have earned from our counterpart is contempt.
On the other hand, if we heal him, then we fight... even if we lose, it's not so bad. At least we showed that 1) we have enough honour to face someone when he's at his best, and 2) that we're willing to fight, but not when someone else decides it. And if we manage to miraculously pull out a win (not impossible, when you watch the mechanics of the quest), well...