Yeah, you technically "can" fix everything in post, but for some fixes, that requires years of repair. imagine going into every frame and manually repositioning them. Yep - that would take a while.
Honestly, you can fix a lot of small stuff in post, but there are just some battles that aren't worth fighting. For this one, you may have to try it this way, but next time, think about the cost of a nice heavy tripod versus the value of the countless hours you're going to spend fixing a few minutes worth of footage. In the end, it's a better investment to start out right.