The Rival 22 medium cage rear derailleur will work just fine for your 10spd setup. Same cable pull ratio. I did the same thing actually, upgraded a Rival 10spd group with a Rival 22 rear derailleur, an 11-32 cassette, and new chain. Couldn't find the climbers kit anywhere available and pieced together the parts for much cheaper from Backcountry and eBay.
Just to add an opinion, it was a good decision and well worth it for the extra range.