Both myself and several others in our club are using BB's in our tires to balance them and they work great. I even have BB's in the 265/75 tires on my DD/towrig, which I recently took a couple off to inspect after several long trips towing my 8,500 lb. trailer.......absolutely no signs of any wear on either the inside of the tire or rim.
There is absolutely no reason why airsoft BB's would not work. Again, you just have to make sure you have enough installed, and you don't have some ridicuously large amount installed.