Is botox into the eye muscle possible to correct a small squint, or might you end up with a different squint?

Yes and yes: Botox will relax (paralyze) the muscle it is injected into. It can also spread and relax muscles that were not supposed to get relaxed. Furthermore, untreated muscles surrounding the injection site can be come stimulated to the point where they are contracting too much. In other words, it's tricky. Make sure your injector has lots of experience with this kind of injection.

Yes: Injecting the right amount of Botox in the right areas can help. Sometimes you can replace one muscle expression with another depending on which muscle groups are injected and whether the contralateral or opposing muscle groups become stronger in response.