As for sodium thiosulfate, I use the stuff sold for treating pool water for salted-paper printing without trouble. I haven't made a silver gelatin print in over a decade, but I imagine that it would work just fine for these as well.
As for using the same trays for salted-paper and cyanotypes, I think that this will depend on how and how well you clean your trays. That said, I have three sets of trays one each for salted-paper, cyanotype and ( when I get to doing them) platinum. I do use the same set of trays for washing all of the prints. (I don't have running water in my dim room, so I use six large trays with 1.5 L per tray, for washing; 10 minutes per tray.)