His jeep probably has a totally different suspensions system in it like a coil spring w/links/control arms. Removing the swaybar will affect that suspension differently then it will affect a leafspring suspension like a K5 has.
I have run without a swaybar for 5 years with no problems. At first you notice a little more body roll & a little more nose dive under hard braking but that is about it. It is even less noticeable if you have lift springs installed. If you have lift springs installed then toss the swaybar and forget about it.
If you have death wobble it won't be caused by the lack of swaybar it will be caused by worn or damage axle or steering components. If your steering system & axle parts are in good shape you shouldn't even need a steering stabilizer.
Harley