Does the wheel actually wobble on the shaft, or is the wobble due to the shape of the wheel itself? If the wheel is loose on the shaft and wobbles, it may be that the arbor hole has worn and/or is no longer round. If it does not wobble on the shaft, and the sides of the wheel wobble, as shown in your video, that would appear to be the result of the shape of the wheel.
I've read a few times here in the forum the opinion that side wobble, even as much as shown in your video does not really adversely affect sharpening, as long as the outside diameter (OD) of the wheel can be trued, presumably using the Tormek Truing Tool. Do you have one of those and have you tried truing OD, which is the only surface that matters on that type of stone.
I've read a few times here in the forum the opinion that side wobble, even as much as shown in your video does not really adversely affect sharpening, as long as the outside diameter (OD) of the wheel can be trued, presumably using the Tormek Truing Tool. Do you have one of those and have you tried truing OD, which is the only surface that matters on that type of stone.