Nice and, welcome
Welcome to !Rust: polish the blades with a rag and some polishing paste (dirt cheap at your local DIY)Scales: to remove scratches you can use a rag and some special polish like "Displex" or watch crystal polish.A fine polish paste from a DIY store does this too, but the "shine" may fade.Be sure NOT to rub over the logo/drawing.General cleaning: use some handsoap and an old toothbrush. (This might remove surface rust too!)Let it dry and oil the pivots with some mineral oil.Open and close all tools untill it runs smooth again.Just my little contribution, other may have better ideas.
I don't think you should remove the scales for cleaning. If they were transparent and there was visible dirt in there, maybe, but otherwise why bother?
Chance of breaking the scales is indeed way to high and not needed in this clean-up.Only remove the scales if replacement scales are easy to find (which is NOT the case here) and when you absolutely need to.Cleaning with the toothbrush and soap should be a serious transformation to start with.I did it a few weeks ago on a vintage Victorinox Mountaineer.It went from "gross" to "like-new" within 2 minutes of cleaning.
Welcome!! nice wenger