Not sure how many of these skills (if any besides Operational Command) are intended to apply to air units, but commanding the Air OHQ probably shouldn't train Mobile Tactics given that it's immobile, and commanding the Air OHQ or its subordinate air units probably shouldn't train Defensive Works given that they cannot entrench. The specialty air-related skills are also conspiciously absent here.
I also want to mention that while Anti-Air Tactics is listed in the manual under Air OHQ-related skills, Air OHQs cannot in fact be given command of ground-based air defense units such as flak formations.

Not affiliated with Slitherine. They added it to my name when they merged the Slitherine and Matrix account systems.