Tree wounds shouldn't be painted with anything. The idea that it 'prevents' damage and helps heal the tree is a myth.

So, no...there is nothing else to be done, other than leaving the tree to repair the damage from the inside.

Here is a link that might be useful: No wound dressings, please!

Yes..painting is better then have it open....it seals it a bit against
disease getting in. I used to use Dr. Farwell's heal and seal but
couldn't get it anymore at the same place, they had Lac Balsam
[Artificial Bark]....I'm using this now for grafting, both are aiding
cuts, damage or what have you on bark from drying out and healing over nicely.
Artificial bark is very expensive, now I'm testing wood glue and see the difference.

Here is a link that might be useful: Artificial Bark