I've eaten about 20 deer that I killed with a .243; I'd just suggest that you quit worrying about it. They fell just as dead as the 20+ I've killed with an '06.
You lay the crosshairs right behind the front leg, low on the chest, and you'll do just fine. Bad Medicine's notion about breaking the front legs isn't bad, either.
For sure, there's no rule against shooting them in the head, either. The ear-hole is a good target; makes for a one-time event.
Mainest, don't go to worrying about it. You'll make yourself your own worst problem. Just shoot the silly thing and go gut it.
By-bye; heading out for camp.