Ohhh.. what if I don't turn on my transponder when getting inside the star system? Would that stop the patrol officers from identifying me? I know I'll still get the minus rep from the "No Transponder warning" but will this at least let me attack/destroy the patrol officer without triggering hostilities?
It will stop officers from identifying you, yes, unless you've been in the system with an active transponder recently. And yes, that will allow you to attack and destroy fleets with only the -5 rep penalty for unconfirmed hostile actions, instead of the instant hostilities for confirmed hostile actions.
Mind you that not running your transponder will result in every fleet making a beeline towards you, and if you turn
on your transponder after doing something that would normally trigger hostilities it
will trigger hostilities since you'll be positively identified as having committed a hostile action. So unless you've got a fleet to outright scare patrols off then after attacking your target you might be forced to attack
every fleet, taking rep hits for refusing to turn on your transponder/unconfirmed hostile actions every time a fleet touches you, until you're able to get out of the system and escape. Once you escape the system entirely people won't be able to confirm you committed the crimes, by the way, even if you jump right back in with your transponder on (I believe, maybe don't quote me on that if you're running an ironman campaign).
So yes, Transverse Jump is indeed going to be your friend.