Slider potentiometers do work. I thought about it. I've already got the gear and rack here. With the two pots, I think I spent about $12, with the stainless rack and cog.
I'd be interested in looking at those slider switches for use. The big thing with this welder is that some of them come with a 22k pot and some with a 47k, so to upgrade, you want either a 25k or 50k for more motion/ sensitivity.
The 25k and 50k pots that I bought (I don't know which knob is on the welder) I think I spent about fifty cents a piece on 4 pots.
Where did you find the sliders? I'd like to know what ohm ratings they come in. Potentiometers range from 5 to 500k in this size.