Well, that depends, I guess. For me, the determining factor would be whether or not I thought it was a sentient creature, dumb creature, or supernatural creature.
The argument for them being sentient is a bit stronger than them being dumb creatures. As far as I know, no other creature has had such a large interest or effort in its discovery, and bigfoot (some variant at least) has been reported throughout the world. If he's real and has alluded becoming someone's wall mount this long, then he's likely a very intelligent species, probably with a 6th sense or some other extra ability we do not have. (In this case I would not shoot, provided there was no agressive hostility on its part.) Everything I've heard about bigfoot seems to suggest that this is the case, or that....
... possibility #2 is that bigfoot is not a creature entirely of this dimension, i.e. bigfoot is a spirit, an apparition, or similar. According to most native American legends I've heard, bigfoot is also an evil/dark spirit, or possibly a shaman or something like that. Recently (this past fall, IIRC) there was quite a bit of noise about bigfoot out on the native reservations in SD's Badlands and surrounding areas (Pine Ridge was the main one, I think). Lots of people - including multiple credible sources like LEOs on duty - have reported increased bigfoot sightings. Again, native tradition says they're evil spirits manifest, so it's pretty surprising that this information even made the popular press, let alone made it off the reservation. It's considered a bad omen to speak of them.
And, if he appears to be a dumb animal, I'd shoot. No telling if he'd drop, though, even with something >7mm. They're apparently freakin' huge (8ft+, 400lb+).