After recovering from his wounds, he became a scout pilot and aerial observer and was dubbed the "craziest pilot in the Canadian military" for his airborne antics.
During his acting career, Doohan took care so that his wounded hand was never shown (during a Star Trek episode where he had to raise his hand to swear an oath, it was actually someone else's) but there are a handful of shots where you can see it. One is in "Trouble With Tribbles", when he comes into the mess hall with a double armload of tribbles. You can just barely see his hand and tell that he is missing the two fingers.
Kirk is Canadian, too. Craziness ran with that crowd??