I'm no drum doctor, but I believe if you want to get those edges smooth and even all around, you'll need more than sand paper. I highly suggest letting someone (a drum tech that can recut and shape those edges with the proper tools) handle that job FOR you. I got a quote from a guy not to long ago for $65 a drum plus shipping. If the drum is worth saving, is it worth $65? That's the question. Refinishing the "LOOK" is not to big of a deal, but the bearing edges will be the difference in a drum you want to play that looks good, or a drum that looks good you can't tune!

I'm also no drum doctor (far from it)    but,  I'd say  if you are REALLY good with a router,  I'd practice a whole bunch on some scap wood similar to what you are working with before attempting this,   but a small roundover bit, set to the correct depth, run over both the inside and outside edge would give you a very nice even rounded edge the whole way around.  I'd recommend a good sharp carbide tipped bit too.   once you have that done,  you could use some light grit sandpaper to smooth off any burrs.
If you've never worked with a router before, I'd suggest not doing this,  I'd hate to see someone mess up a drum on account of my suggestions...  

oh yea,  like 563 said,  you'd  have to straighten the edges first if they are as bad as you said    before taking a router to it

Oh Yeah,  volunteer to do your friends drums first.  A little experience goes a long ways.