As far as I'm aware, you have three choices for huts:
1. Nogodon shelter, which sounds pretty big
2. Piagol Shelter, which is smaller but pretty out of your way - you have to hike down Piagol valley for a bit over an hour to get there, but you can return to the main trail a slightly different way
3. Baemsagol shelter, which shows itself as a 40 minute walk downhill from Tokkibong, but I'm not sure what that translates to when you're going uphill.
Hope that helped