You can't. He is there to help you, even if his constant presence is sometimes annoying.
You can't play "as" Nate, but everywhere you go on the island, he tags along.
Nate's locker is on the second floor of the school near the Science Room. It is obviously stuffed full of junk. The combination is on the comics that you assembled into a strip. Use the number (9305)...
You get the keys from the lobster guy. Then you ride. Jump when necessary to reach the island. Be faster than Nate!!
You do not play as Big Nate. He accompanies you around most of the island, and races you on the jet skis.