Lube your pivots with sterol or some other high quality, rust inhibiting oil. Dry your razors thoroughly after use and find a place on a shelf to let them dry (partially open) before putting them away. Mine sit open on a shelf (a high shelf as I have an 8-year-old daughter) overnight before putting them away when I take out the next days razor.

Yes, I know I've not told you how to remove existing rust, just prevent it. If the rust is beneath the scale, I don't see how you can get to it without removing the scales...sorry.

Ed