Thanks for the helpful information. I had no idea you needed to be a sub volunteer in order to pick up welding. Does this mean that you will need to be a dive welder? How likely would I be able to pick up this skill? I know you said that there are only 1-2 per class, does that mean not a lot of people go for it? Or that it is really selective?
Each boat is (was?) required to maintain at least two MM's who are qualified emergency welder. As HeavyD stated, this is solely so that the boat has someone to weld some metal in a dire situation. You won't be welding the side of the hull and the chances of you actually welding anything onboard a boat while underway are near 0. You'll weld something like once or twice a year, in a shop at the sub base, to prove that you still know what you are doing.
Realistically, welder will work like most collateral duties: If you show up to your command and the division needs a welder, they might send you to weld school because they're not 'losing' anyone by sending a non-qual. There are a handful of other specialty schools you might get sent to.
Welding for the Navy is mostly done by shipyard workers, who are civilians.