Please allow time for the big cactus cutting to heal (callus) before you pot it up. Most people say a couple of weeks stored in a shady location is enough. The size of the exposed "wound" on this cutting is small since the diameter was small so it should not take long to heal. Larger exposed cuts take considerably longer to heal....sometimes months.
When I pot it up I use bamboo stakes to hold it upright and I do not water for a week or two to encourage rooting. Then I water infrequently since it takes longer for the pot to dry when there are minimal roots to take up the water. So keep to the plan of watering only when necessary (the soil is mostly dry, but never bone dry). New roots do not like to "completely dry out".
That said: Do Not Overwater.
I start my new rooting in shade (bright light), never in full sun. Once the top shows new growth the plant can be moved gradually back into full sun.
