You could try the .22 but have you checked the price of ammo lately? And unless you've got a scoped rifle, it's gonna take a lotta shots to get enough down to make it worth the effort.
Repeated doses of .22 LR directed at the base will take a few chunks out pretty quick.
Do not go digging into the old ammo section of your gun closet for the 3"magnum, copper plated, buffered #2 lead shot and fire it straight up at the base of the mistletoe clump.
It will both blast large chunks of mistletoe off, and drive you into the ground like a tomato stake! (Ask me how I know!)