. I'm going to let the cutting sit out in the sun for a bit so the wound will scab over and then plant it.
Dunno about your climate, but i own quite some cactus, ad usually when i want to root cuttings i let them dry for a month in a light shadow. Full sun usually can dry smallest one too quickly, wich can slow the development of roots. Full shadow instead can be detrimental ro the drying of the cut, and can promote the growt of the cutting "out of the soil" with bad results.
After a month i put them in pure sand, and i water them very ligthly, maybe once every few weeks (the quantity of water that can be dried in a day). The water, if very moderate, can promote the growth of roots. Too much water instead will bring the plant to rot.
They usually root in the following weeks.