Burning a gallon of LP produces almost a gallon of water vapor (along with about 14 lbs. of CO2). If not vented, water vapor will condense on the coldest surfaces which will be your outside walls in an uninsulated or poorly insulated shop.
I run a dehumidifier 24/7 in my basement shop during the summer and pull out about 2 gallons of water a day. This, in conjunction with the central A/C, keeps the house and shop at around 50% RH and I do not have a significant rust problem. If I let the humidity creep up, I start to see rusting.
IMO, if using an unvented burner in an enclosed environment, proper consideration must be given to venting and air exchange. The problem is that bringing fresh air which may be -20ºF in the winter is counter intuitive. Maybe it is ingrained from childhood when my mother scolded me "Shut that door. We're not heating the outside!".
One solution would be to make a heat exchanger for the exchange air. Some years ago, I designed a heat exchanger where the outgoing warm air would heat the incoming air, capturing some of the escaping BTU's. It never got built because the need disappeared ( I heat with wood and my exhaust air goes up the chimney).
Here is a concept sketch. The sketch is essentially a floor plan withe the height suitably chosen for the volume of air required. The walls between the intake and exhaust chambers would be made from a thermally conductive material while the flow reversing baffles can be any suitable material. As intake air flows through, it will be progressively warmed by the heat removed from the exhaust air. Ideally, the intake air will be almost at room temperature as it enters the room while the exhaust air will have lost almost all of its excess heat value.
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