I would never opt for a chemical solution where a mechanical one will likely work.
I would use Scotch Brite and/or aluminum oxide (sandpaper) to "rough-up" and then "smooth down" the slide. Mechanical stain removal will not significantly affect the integrity of the slide unless you remove a large amount of metal...and with Scotch Brite/ sand paper, that will take a while.
Chemical treatment is a whole 'nother animal. Unless you have a chemical engineering degree, you have no idea what short or long term effect chlorine or any other chemical will have on the stainless steel.