Hi rrsteve, I grill/smoke lots of oysters all winter, this year I went through 3-1/2 bushels... I got plenty of zinc now.
Anyway... oysters (and clams, mussels and any whitefish) need a delicate smoke like cedar, alder or apple. Hickory, oak or mesquite are too strong and will overpower the flavor. I put them in the smoker for 20-30 minutes at 225°F, just until the edges are curled and the centers plump up. Do not let them overcook or they will get tough. If you are shucking your own, cooking them on the half shell makes a nice presentation. If already shucked, use a shallow pan and spread them out in a single layer in their own liquor.