One of the problems with arc welding is you need to generate an actual arc. In atmosphere, this isn't a problem because the electricity is arcing through the gasses to complete the circuit.
In a vacuum, like outside of a spaceship, this is going to be a problem. No gas to arc across, no arc. No way to complete the circuit. So this depends on which side of the door your character is on and what he has to hand. Break down the problems one at a time.
You could simply handwave an arc welder aboard as emergency equipment. That's the easy out. Justification could be that gas-based welding (I imagine) would be way more dangerous aboard a spacecraft. While current based welding systems do not share the same dangers, they have their own set of problems.
If you don't want to give a narrative excuse for having a welding rig on board, you could have your character MacGuyver it. A welder isn't really all that complex from an electrical standpoint. I don't have an electrical background but I found this paper on what it takes. I have a welder that can run off the same circuit as our clothes dryer so I imagine the ship will be able to supply an adequate amount of power. So your guy breaks down some non-survival-based equipment like a microwave oven, adds the extra stuff he needs and he builds a welding rig.
If your guy has to go outside the ship he might need some sort of medium that will stick to a surface and allow electricity to arc through. I think the gel depicted in the show "Firefly" would be an imaginative way to start
