Yes, I would.

1.) I can always use the money.
2.) If we're talking world class, everyone would know it's my buck anyway, so I wouldn't have to prove anything. Which leads to the next point:
3.) Everyone would know I had it. Theft of world class deer heads is a real concern and not one I would want to deal with. (and as someone mentioned earlier fire)
4.) I would sell to some sort of public accessable entity, not a private collector.
5.) I would retain all rights to the deers image and any royalties from replicas and promotional photos. (I can always use the money.)
6.) I might have to have some sort of stipulation allowing me to borrow it for certain shows. (I can always use the money.)
7.) A good artistic replica will be sufficient for my needs. I'm not going to take it off the wall and fondle it. If it looks real it will be a sufficient reminder to me. My memories are not sold with the head. Only old age can take those.

I have the same opinion about any kind of expensive heirloom I might find or inherit. No matter what the sentimental value I can't afford to have that kind of money lying around my house to be stolen, or destroyed. I get upset enough when I break, loose some cheap item around the house let alone something of that value. Seems like more a burden then a blessing.