It’s not clear how you heat this shack, but if you built it that air tight you have to have a vented heater of some kind. Don’t even consider a ventless heater, they create a lot of moisture into the air.
I ran a ventless in a less than air tight shack for years with no problem, but when I shut the heat off and there was moisture in the air….the inside turned to 1/2″ frost on everything.
Fans work wonders. I’ve used a minimum of 2 fans for a shack from 10-12′ in length. The fans dry the air very well, even in the old ventless shack. I can run a couple fans for several days on a deep cycle battery (I often heat the house to 50 degrees most of the winter while I’m not there).
Putting a vented heater in is not much work, and there are good cheaper ones out there for a few hundred bucks (Menards). In fact my friend and I had to install a new vented heater on the lake last year in sub-zero temps with minimal tools to save a fishing trip. 