For just small spots on stainless, the baking soda paste should work well enough to scrub away any loosely attached red rust. On stainless steel, I wouldn't worry too much about whatever remains beyond that, as red rust won't likely take a strong hold in the steel anyway.
I've liked using the wooden sticks from popsicles or ice cream bars for a scrubbing tool inside the bladewell of folding knives. Can also buy the sticks in bulk in the crafts section of stores like Walmart or Hobby Lobby as well (usually labeled as 'craft sticks'). You can whittle a point on the stick to reach into tight corners of the pivots with that. Could be used in conjunction with the baking soda to scrub the inside face of the springs. Baking soda will completely dissolve as well, when some water is added. So there's little risk of any baking soda grit remaining in the pivots after using it. Just rinse it all thoroughly. And baking soda isn't hard enough to be abrasive on the steel itself, but only on the relatively soft rust on the surface.
I have a Victorinox SAK that was left in a tool box in the covered bed of a pickup for several years, in a wet/humid climate. It rusted enough to make opening the blades difficult. It was more extreme than just few spots of rust. For that one, I soaked it in WD-40, then wrapped it in paper towels also saturated with WD-40, and sealed it all in a zip-loc bag for a few days' time (4 days or longer, IIRC). That helped to soften and loosen up the rust in the pivots, which then made it somewhat easier to open the blades (with the aid of pliers). After that soak, I continued to saturate it with WD-40 while opening & closing the blades to work the rust out further. So long as the WD-40 was flowing red/brown while doing that, I kept spraying it. After it started running clearer, I then gave the whole thing a bath in warm water with liquid dish detergent and flushed out all the WD-40, rinsing in hot water (evaporates more completely to make drying easier), then oiled the joints. I don't think you'd need to take such extreme action for your knives, based on your description of the rust. But I include this just as another option if you feel it can help.