I have somehow managed to beat Mawile using only one move (so two moves left) on stage 51 of Pokemon Shuffle on my second attempt (where I only had one move left). I know that Mawile has a Mega a little later on, so I want to catch it. However, I was not able to catch Mawile with my 78% chance I had, and I doubt I can beat Mawile with one move again. So is it worth using a Great Ball, which I am capable of buying 4 of right now (11280 coins)?
Yes, it is. Mawile is well worth it, as he will be your only Steel-type Mega for a long time. He will be a valuable asset. You wil still have more money after buying a Great Ball.