i play tennis and badminton.
To be honest, I've play badminton a lot longer than tennis. Badminton to my home country is like soccer to Brazilian.
A lot of my friend from my home country here plays both tennis and badminton. Tennis for the summer and badminton for other season.
At first, yes badminton does affect my tennis game. When i got into badminton after tennis season i hit like tennis and not doing enough wrist movement. After a while i'm getting used to it and play normally again. and vice versa
This is my opinion. If you're just recreational or club level player who play tennis to enjoy life. Then i think doing other racket sports is not a bad idea. Sport is sport after all, it keeps you moving and healthy.
Granted, you may take a while to adapt, but you will get the strokes back eventually. You're injured and have nothing to do anyway, squash will keep you in shape, and way better than doing nothing at home.