I figured out how this can work.

Put the girl on her back 'tits up' and hang her head upside down over the edge of a bed or something. If the dude can spread his legs far apart enough she can probably wear a big hat.

Also other hatted blow jobs might be cool, top hat is obvious but how about that beanie/crown thing that Jughead wears?

I have seen baseball cap.

Military gear would be awesome, like one of those tooth brush crested war helms.

Cowboy 50,000,000 gallon hat.

Wizard hat.

Point being, as usual, things must be made as awkward and stupid as possible.

Party hat.

Wigs do not count as hats.

One of those Australian cork hats that repel bugs would be fucking amazing.

Hey ladies! Put your blow job hats on.

Visors count, like those old timey accountants wear in movies.

Head bands do not.

Pots and pans count.

A indian feather head dress would be perfect.

Bandana is not hat.

I actually own one of those horse riding jockey helmet things. That would rule as a blow job hat.

Silly hats + blow jobs + whores = satisfying.