A properly fitted revolver should have a minimum end shake of .001" to a maximum of .003".
Since you have .007" you may need a fix. You want a shim bearing that will bring the measurement down close to the minimum.
To do a proper job, there's more than just dropping a bearing in. The end of the cylinder shaft should be trimmed to remove any unevenness by using the tooling Brownell's sell. This also allows fitting "in between" sized bearings for a perfect fit.
However, given the choice between putting a bearing in without trimming the shaft, and living with the end shake, I'd put the bearing in.
The bearing fits inside the cylinder, beneath the cylinder yoke. The cylinder is completely disassembled and cleaned, and the bearing is greased and dropped into the hole in the center of the cylinder.
I STRONGLY suggest buying a copy of Jerry Kuhnhausen's book "The S&W Revolvers: A Shop Manual" first. This is money WELL spent, and has the most detailed instructions on correcting end shake ever published....Cheap at the price. It also gives complete instruction on how to disassemble without damaging the delicate parts.
Side plate shims are used to repair revolvers with badly worn hammers and triggers, where the parts are so loose they "wobble" excessively.
The shims fit between the hammer and the side plate, taking up the excess side-play.
Yoke bearings are put on the lower shaft of the yoke that enters the frame. These are used to correct yokes that have worn, and are moving back and forth.
In actual practice, side plate shims and yoke bearings are very seldom needed on the average S&W.