Dependig on the room size, an oil radiator is the safest way to go for anything under 20x20 feet. No flame, if it tips, it can't hurt anything. Run it a while before hand and you're set.
We have an inefficient furnace in an 1869 house. Laff and plaster walls. Poor insulation almost everywhere that hasn't been thoroughly renovated. With the gas prices so high, we've taken up using only the radiators. The higher electric bill for the entire winter is small potatos to the first winter month's gas bill in this place.
If you are dealing with a drafty workshed, like one that has gaps in the planks or such, you'll need something that can crank out the heat. Torpedo heaters work well with ventilation, so long as it's a newer one with the ceramic flame-shield to prevent exposed flame.
Effective safety requires you assume the worst can and will happen. Imagine dropping a can of flake powder in front of an open flame heater ::shudders::