Get a 14t DX Sprocket. Then get a new chain. Will work a treat and you'll have change from £15 rather than getting king kogs etc.
The K810 is the 'cassette' narrow version, its just the same as the bmx one but narrower, so I can't see it making any difference.
I would never run a cassette cog on the rear, its silly to constantly replace your chain, when your running the risk of it slipping off, which could have all the same problems as the chain snapping.