At one time I used to have thin plasticard packing pieces glued to the GW wheel press. This works fine for wheels with a boss. But some wheels do not have a boss. I now use removable insulating tape to support the wheel rims if there is a boss. The wheel rims should bear on the plasticard/tape spacers and not just the wheel spokes. If you want to try and take some of the stress out of using the GW wheel press, I recommend Alan Sibley’s article in MRJ151 (2004) showing how a simple jig can help.
As for the GW wheel-puller separating the spokes from the wheel rim (tyre), this has happened to me too many times. I use a thick (0.8mm, more would be better) piece of circular brass with a 1/8” slot cut out for the axle (see the image below). Mine is 22mm diameter but should be greater than the diameter of your largest wheel. I still find this a pig to use successfully as the puller hooks tend to slip off. Does anyone have a better solution (do not suggest a lathe!)?
I must admit that I now have an (expensive!) aversion to re-using driving wheels that have been dismantled. At least one chassis required a rebuild after re-used drivers slipped on their axles and made a mess of rods, valve gear and more. The plastic that Alan Gibson and Ultrascale use in their wheels seems to deform slightly on second use.
Avoid wheel re-use. Get it right first time!