OK ... this was my recent cheap DIY paddle silencing hack. It worked ... although no idea how long it will hold up. Also note .... did not spend much on our paddles, so little risk if things went poorly.
First ... what thin and cheap "rubber" to try first. Some of the table tennis rubbers cost more than our starter paddles

... so let's call those potential future experiments.
Found this on Amazon ... passed the cheap ... so bought it.
One thing I liked in the description was it already had the sticky back ... so no glue. Also ... claimed it would lead no residue if you peeled it off. I was doubtful about that ... and no way I was going to risk hosing wife's "pretty" new red paddle. So I tested it on my paddle with a small piece, and peeled it off. Nothing ... didn't even need to wipe it off with a wet paper towel or something. I can't speak to once it's been on for a longer time.
The sheeting came in a roll ... so spread it out and put the paper side up so I could outline the paddle for cutting. If I stick to this ... I will come up with a better method to be more precise of matching inside the paddle edge guards.
Went ahead and cut out for both sides of both paddles ... knew this stuff wasn't going on that red paddle until we went and tested mine.
Need to do one more thing before you stick the Pickleskins on ... the sheet came in a roll. You need to take the memory coil out ... only took a few minutes and was good to go:
So off to test. On wife's side the annoying clack, and my side a most pleasant tennis-adjacent thwak/thunk. OK ok ... I know ... the rules man, the rules ... you just created a spin and power Picklegeddon. So I tried massive topspin. Nope ... I would say marginally more topspin, certainly not enough to **** of my wife, which I have to admit was a bit disappointing. So what about this new raw unleashed power imparted on Mr Wiffle. Nope ... perhaps even slightly less due to the "sponge" and insulating (this product advertised to dampen noise btw) part. I think the slight increase in paddle weight, but will probably a little less bounce off that paddle rocket science fiberglass surface was a wash ... about the same power. Meaning ... if one brand new Pickleballer first attempt at muffling the wiffle was successful, then the USAPA argument that it can't be done without vastly changing the game ... just might not be true. Just sayin ... come on Pballers ... keep on open mind. You don't want to be those annoying noisy people ... do you? Don't answer that.
Which brings us to the real critical test. If rules girl wife ... who already isn't to crazy about husbands paddle "cheating" ... what happens if we actually play with others and they don't like it. I told her when we get to the point we are playing for $, we can buy a second set of $37 paddles without the cheat sheets

, and just pull out the legal ones. And ... I think this was
@Lorenn 's great suggestion ... maybe also carry an extra paddle of two with the cheat sheets, and let them try it if they would like. It's a Quiet Mr Wiffle Ground up movement ... one park, one community center, one couple at a time. Has to start somewhere ... needs to happen.
Anyway ... where was I ... oh, the critical rules girl wife test. Let me put it this way ... I had a hard time getting my paddle back.
https://imgur.com/nJIa4Mi
One interesting thing was Mr Wiffle left a mark on the rubber. It was very clear where you hit the ball on the paddle face. It was at this point my thinking that I needed to extend the handle was confirmed. Tip hit paddle hits do not carry like the forgiving modern tennis racquet.