I would remove the skin beforehand if you don't want the skin on. Get a filet knife, lay the salmon skin side down on a board and slice it off, starting at the tail. Once you get the tail started you can pinch the skin with your fingernails against the board to hold the filet in place. It doesn't take long to get the knack of the correct angle to hold the blade, where you don't leave meat and don't cut the skin.
If the grill is clean and oiled before you put the fish on you should be OK as long as you don't try to flip it too soon (like cooking in a SS pan). Of course, as the fish cooks and especially with a big filet..... flipping requires a little finesse. It's more of a roll it over, so leave yourself room.
Or, just start buying salmon steaks rather than filets