If it were me, I wouldn't do that.

Literal

I [if-だったら], like-that-は do-not [reflective-な].

そうはしない ('not do that way') contracts そうする ('do that way') with the contrastive は inserted — emphasizing 'in that way specifically, not' as opposed to other ways. A hedged disagreement or gentle disapproval. The reflective な adds soft self-directed musing.