Short swing trail

Hey guys, I'm going up to pharaoh lake wilderness in may for a three nighter with my son. I think I'm going to come up Thursday afternoon and hike in to tubmill marsh leanto. The question I have is if that leanto is full are there any spots to camp nearby? I know there are none by the leanto but what about down the trail? The next day I'm going to pharaoh lake leanto 3,4 and Saturday we will head to rock pond with sunday the hike out back to short swing trailhead. I'm guessing we will be coming in the dark so I want to make sure I can get a camping spot without to much trouble.
Thanks