Here's the deal: Switching off an inductive load is much different than switching off a resistive load.
When you switch off a resistive load (like an incandescent bulb), the power gets cut, all is well. When you switch off an inductive load, the inductor has a good bit of energy built up in the magnetic field around it, and will try to dump that by raising the voltage... and if there's enough current and inductance, the voltage can shoot up to thousands of volts. That's why, when you unplug the vacuum cleaner while it's running, you get a nice, fat spark - but unplugging a 500W halogen light doesn't do the same thing.
Well, that arcing takes its toll on the switch contacts, as you can imagine. Over time, the contacts will become degraded and conduct more poorly, so heat production becomes an issue. Eventually, they can either burn up, melt the housing, or in extreme cases, even get welded together. That's why relays can eventually "stick on" when they are controlling inductive loads. Switches designed for inductive loads are made with contacts that are much more resistant to being damaged by the inevitable arcing, but ENOUGH arcing will still damage just about anything.
So: When a switch tells you how many HP it can control, it's doing so because motors are entirely inductive, and if you know the HP of the motor, you have a rough approximation of both the current and inductance of the load.
Your welder, having a nice big set of coils inside, is an inductive load. And it draws a lot of current. You have two choices... buy a low-spec toggle, and plan on replacing it again in the future, or buy a high-spec one and not worry about it. When I've run into relay/switch problems with inductive loads, I've always replaced them with units two to three times larger, and have never had a problem after that. When you buy a new toggle switch, pay attention to the voltage rating, many are meant for low-voltage only.