It would interfere with testing for rabies if the head is missing or mishandled. I suggest this because they generally kill an animal that was agressive and bit a person to check for rabies. ref https://www.dshs.texas.gov/sites/default/files/IDCU/health/zoonosis/animal/bites/information/bite7-20.pdf
As to the dump them etc, there is also a golf ball brand “Cougar”. Was playing with a guy who mentioned their slogan should be, “there’s nothing like pounding a Cougar!”.
All wildlife,up north and down here, is property of the state.
It doesn’t matter where you get it.