Is there a HARBOR FREIGHT TOOLS store in the Chicago area? If so, go there and buy a set of their ORANGE handled 'Pittsburgh' pliers (probably about $20 when the are not on sale, and under $10 when they are).
The inside of the handle side of the hinge on both the needle nose & lineman's pliers has a "fluted" surface which is perfect for gripping & removing rounded nipples -- a great discovery that I made a few years ago -- no other manipulation of the wheel is needed (however, see below)...
Now, there may be OTHER brands of pliers that can perform the same task ... I guess if I track down my older lineman's pliers I could look-and-see (but, it never seem to lend itself for the task) ...
The other option is to completely detension the wheel (which you may want to do, anyway), and then you can use almost anything to remove the nipple.
BTW. If there isn't a HARBOR FREIGHT TOOLS store within 20+ miles of where you live, then you can use mail order (which is how they started).