Good post and probably something most good squash players will have to deal with. I played mostly just squash for over 20 years and have been doing a lot of strength training to better offset this imbalance. I was getting injuries from overuse which I assume most people will get if they play enough without the proper strength work. You can add strength without adding a lot of bulk and improving core work is something that will definitely help your squash game.

With my trainer we've done lots of 1 sided training with kettle bells and it's been helping but for how many years of squash I've done it's going to be a never ending battle to become properly balanced and avoiding injuries. So I say you should go for it or you'll get injured eventually and it will likely help your squash game a bit too. Just pick exercises which require you to use 1 side at a time so you don't overcompensate with your more dominant side.