You make a valid point about the safety of conductive grease anywhere near the air path but Vaseline is not a solution, it will make the electrical conductivity issues worse.
As I said earlier, Vaseline was and is used in East Germany for several decades (!) for exactly this purpose (to prevent oxidation of aluminum conductors), without problems.
Also Phoenix-Contact has such a product (with more secrecy, but quasi identical) in the offer. You just fill up e.g. Wago terminals (completely), before you plug in aluminum conductors. The carbide-parts break up oxidation, the vaseline keeps air and water out.
It is important that the connection is always made with a strong contact pressure, as here in the TM.
This displaces the vaseline from the actual contact surface and prevents air (oxygen) from getting to the active connection area.
In addition, the tungsten carbide is a very good conductor and would maintain a good conductive connection, even in the case of insufficient pressure or already oxidized surfaces.
And I may remind us that exactly this problem already exists:
The contact resistance of the contact point in the Tinymight increases due to oxidation ;-)
I have taken for granted that you should not apply a larger amount than absolutely necessary.
Personally, I would probably after (very thin) application and first screwing again remove the lid and wipe away all excess Vaseline (everything that was displaced to outside the contact point).
However, I also think that even a slightly larger amount of Vaseline would not do any harm at the site, the wood would simply absorb it.