I would try buffing just the edge to see if you can clean up the rust. If you don't have a buffer, a progression of some abrasive papers and some
Maas polish should do the trick. You can get the Maas at Walgreen's, among other places.
As for whether you should clean it, I think you have to get the rust off or, at the very least, stop it. My understanding from spending time on the Razor forums is that it doesn't hurt the value to restore it. Which seems to be the opposite of what you'd do to the value of an old knife. To sand it you can wrap the paper around a hose of similar size to the curve of the blade. Just watch out for your fingers.
If you aren't going to shave with the razor, there's no sense honing it. Of course, all of us cool kids shave with our straight razors.
Check out this link to the
Straight Razor Place for more info.
Here's one I restored and shave with. I used lots of sand paper and a buffer. ;