Sounds like a cool idea! It's a great mod that arguably enhances the original design. The artwork makes it clear that you're punching the Big Shot when you hit the target. He's recoiling but nothing is actually hitting him so you have to use your imagination.

You'd want to put the Big Shot on some kind of spring mount so he doesn't get subjected to much shock and recoils deliciously from the impact. But there isn't a lot of room there so he couldn't spring back too much or he'll hit the mixmaster housing.

Any idea where you'll source a glove? Possibly find a toy that you can cut the arm off and use that.

Could you re-use the coil arm as part of your new Big Shot mount? You'd probably have to make a new coil arm for the glove anyway so that it can be positioned a bit further forward.