It will partly depend on the scale material - gotta be sure whatever you put on won't hurt those. If they are savable, that is; if they are trashed then it won't matter either way.

I'm not sure I've ever seen a razor rust shut, so I'm very curious. Is it due to rust in the pivot area causing extreme friction? If that is the case, I have found that just a drop of mineral oil on each side really helps. It will make the friction between the blade, scales (and washers, if they are there) strip the rust right off. And whatever oil is in there keeps working over time, always taking off more rust as you open and close the blade. The only downside is that oil in the pivot can attract and hold dirt and dust and whatnot.