Cacti root from elevated humidity levels underground.
So what seems best is to have a material that holds water (it doesn't have to be much) and slowly releases it.. and on top of that you would want a dry layer which slowly has the more humid air passing through going up..
Always prevent sustained moisture contact with the cactus. Let it callus well first and perhaps just suspend it right above the dry layer to be even more careful. Also ideally have everything go dry frequently before making moist again, to prevent rot.
Similarly i root cacti like peres (which yes root very very easily) not in water which imo sucks, but just in a glass with a piece of moist tissue in the bottom and dry tissue on top of that. With the cactus placed right above that, it should root alright.
Note that it should be a certain temperature/season for the average cactus to want to root, i think. Don't try it in a cold season.
I tried perlite and vermiculite but didn't like it personally. I really don't think you need it. Vermiculite retains water too well and perlite releases it too well in my opinion. The humidity needed probably is better to be much more subtle.