If it's skipping up to a lighter (more teeth) gear, there's either too much tension on the der. cable (unless it's a rapidrise derailleur, in which case there would be too little tension) or the derailleur's damaged. I also doubt that the cassette's wobble is causing the skipping. Try an undamaged derailleur off of another bike if possible in order to avoid having to buy one just to find out whether that's the issue.