This is not a silly question, of course. I'm not an expert, probably, but I also cut off my adeniums. I do not process the cutoff, the branch dries up by itself.
I cut the branches differently. Not all at the same time.
I cut the old branches one at a time. I look where the plant has the kidneys. And I'm doing a cut on this place. Then I wait, when there will be new young branches. And after that I cut off another branch. I suppose that the plant must have a balance between the roots and the crown. Especially if you have a hot climate. Maybe I'm wrong, but I think your plant withers because of improper pruning, but not because have not processed the cutting site.
Sometimes I buy phalaenopsis on sale. Not because of the small price, I just regret the plant. Such orchids can have small rotten injuries. In these cases I use cinnamon powder. I just clean the damaged area and put the powder in place of the cut on the plant.
Cinnamon is a natural remedy for mushroom diseases and prevention. But with severe damage it will not help.