If this same scenario were mine, I would be ready to tag the animal, but before doing so I would call my local game warden and tell him the deal. I would also tell him that I am ready and willing to tag the deer, but wanted to see if he wanted to look at it or if there was a way for him to collect it for any sampling they may be doing or to help feed the hungry. If he says no to both of those, I tag the deer. That's ethical.
...I am not skilled to understand, what God has willed, what God has planned, I only know at His right hand, stands One who is my Savior....