If those are normal plastic, for any surface dirt, you could use an ultrasonic cleaner with a mild detergent or a toothbrush. It won't take out the yellowing of the old plastic though.
Buffing them carefully can also remove some of the yellowing but I'd be really really careful - wouldn't want to "round-out" the nice "engraving" on those old scales, and I'd rather have them yellowed than damaged.
I would try a mild natural substance like a paste of Borax and dish soap, and a toothbrush to scrub them down. Maybe try a bit of oxyclean paste on the underside near the pin holes to see if it does anything to harm them and then proceed if there are no issues. It will definitely remove the dirt and debris and perhaps do a little something to remove the yellowing. I agree with Khay, better yellow than ruined.
Have you done a "hot pin"test,to see if they are ivory? I have an old german razor with a rope twist design. I assumed they were plastic until someone showed me where a tiny chip had been removed. Probably for testing. Anyway my friend assures me they are genuine Ivory. Either way,you have nice scales.