Water pump pulley shakes and wobbles.

A loud noise started coming from my sonata that sounds like the engine is cracking clanking. I checked under the hood at AutoZone and one of the reps noticed one of the belt pulleys was wobbling and shaking side to side. I did some research and took a close look, and now I believe it to be the water pump pulley.

My question is, can I replace the pulley without breaking down the timing belt and simply loosening the tensioner on the alternator? It's beyond my mechanical skill to dig that deep, but I could probably loosen that tensioner and take out the pulley without moving the belt too much. The car was bought for $2400 in 2012, so if I have to take it to a mechanic, the most I'd be willing to pay is about $500, otherwise I'd rather buy a new car. Will this repair job fit into that price range at a mechanic's shop?

The sound it makes: http://vocaroo.com/i/s1L9eiM9BC0l

Look at the attached picture of what I suspect is the pump pulley and tensioner