What is a minimally intrusive way to move a wire that is in a wall 3.5" to the left?
You could always pick up a 1-Gang low voltage old work bracket like this...


Cut the hole to install it, which should give you enough space to grab the wire from the previous hole. Then finish it off with a wall plate like this.



This is sort of an ugly wall plate (used for example only), they make nicer looking ones but I couldn't find one with a quick search.  They used to have some that also had a way to mount the speaker built in, but I'm not sure if they still make those.

One of these snap-in types might look better.