These are not exactly the tightest guns on the market, and they do have some play in the cylinder.
But if it's not affecting the function and accuracy, you might be better off leaving well enough alone.
But, if you are like me and like to play with stuff -
Does the front to rear play in the cylinder occur when it's loaded with ammo and closed?
The reason to ask is that the rim of the rounds take up a lot of slack.
Reducing this slack for an empty cylinder can cause problems when the gun is loaded.
To reduce this slop, if required, try a shim over the shaft of crane, where the front of the cylinder butts up against it.
A very thin washer, of suitable diameter might work.
When you say the cylinder is wobbling side to side, is that a rotational thing or a left to right one.
A rotational one can be caused by the dimensions of the slots in the cylinder too large for the cylinder stop bolt.
Or by the stop bolt being lose in the frame and moving a bit, side to side.
A left and right one can be caused by a bent ejector rod or a crane that's lose in the frame.
Hope this helps some.
Who says revolvers are simple?
Walt Kelly, alias Pogo, sez:
“Don't take life so serious, son, it ain't nohow permanent.”