If you have the ammo, they're going to think you have a non-declared gun which means you could spend the day at the checkpoint while they search for it.
Had a friend returning to Alaska with a bunch of empty shell casings for reloading while he was home for the summer. He'd left the guns with friends in Washington. When they found the empty shell casings (and it's legal to transport them without declaring them) they spent hours searching him for the guns they of course never found.
Leave the gun home or south of the boarder, you don't need it. If you really think you do,buy a box of ammo up there.
Bill