While your answer is the truley correct one from a legal standpoint, it doesn't respond to the original poster's question... Which is "What would you do?"
Your answer would lead us to believe that you would wait for the authorities....
Would you?

I would dispatch the deer if I could do so considering my own personal physical safety. A handgun would be perfect, or a 2 lb ball peen hammer would suffice.
Cruel though a hammer may seem to those who have not dispatched an animal like this, it can be more swift and "clean' than a decently placed bullet.

It is an interesting dilemma. Hunters that pursue and kill deer wanting to help ease the same animal's pain when fatally but accidentally injured.
I have put a few deer down when it was illegal. I also know that it was morally responsible and ethically unquestionable. I have hopes that if I had been caught a good judge would have offered me a suspended sentence or at least an appropriately well thought out punishment.
Either way I'd accept it b/c I accepted the possible punishment when I knowingly broke the legal stricture even while obeying my moral compass.

I don't think there is a right or wrong answer that fits all. There is each persons decision.