A couple of notes here. The owner of the store I work at, Overture Audio in Ann Arbor, MI, discovered Silly Putty at least a few decades ago, long before Zerodust and others. He reasoned that some putty type of material would grab the little particles off the diamond that we see under our high powered Wild Heerbrugg lighted stereo microscope that brushes don't completely remove. So he tried all kinds of things from modeling clay to caulking putty to Silly Putty and others. Of everything he tried Silly Putty left no residue and resulted in a gleaming stylus. I put this on a few forums a number of years ago and quite a few people have used it in various places.
One customer who had used Silly Putty tried Zerodust and brought it into us saying Silly Putty worked better. We never spent any real time trying the Zerodust. A while after I posted about the Silly Putty I read someone suggesting Bergeon Rodico 6033 watch putty so I bought some but thought it wasn't any better than Silly Putty. Then while I was looking for the Rodico online I bumped into a watchmaker's forum where the question had been asked of what to use to remove fingerprints from crystals. The questioner had tried Rodico, both types (this is where I found there was a 7033 in grey rather than 6033 green) and wasn't happy with the results. One of the members said the best thing for that was Rub Off, a dark blue putty I think originates in Germany. With this new information I decided to duplicate the tests the owner had done decades back. So I bought some Rub Off and some Rodico 7033 and put them up against Rodico 6033 and Silly Putty. Silly Putty definitely left very little residue and easily less than either Rodico (which were about the same) but the Rub Off was even a bit better.
So my suggestion has been Silly Putty works just fine as long as you make sure you get the right one. You have to stick with Original Silly Putty which is pinky orange. The glow in the dark and other colored versions are different and are to be avoided. But if you want the absolute cleanest stylus the Rub Off is a little better. It is also a bit stiffer so you do have to be careful with it.
I have seen a number of styli with built up gunk around that stylus that is hard to remove. Most of these are from people who don't clean their styli or who used some kind of liquid cleaner (obvious by a coating of some crystalline substance on the cantilever). I haven't seen any like this from customers using Silly Putty. The only thing that effectively removes it is Linn green paper. In my stylus cleaning I regularly use Rub Off interspersed with occasional use of green paper. Many customers do the same with Silly Putty and green paper. I have an old Discwasher SC-2 stylus brush that I use to get off fluff balls. It is also decent at getting gunk off but not as good as green paper. Unfortunately they haven't been made for some time and they should never be used with the liquid that came with them. But having tried a number of the other little stylus brushes I have found none of them even good at getting loose dust off.
Here's a link for the Rub Off:
https://www.esslinger.com/rub-off-compound-dark-blue/