Noun phrase converted to verb, is a hyphen needed?

In the "air kiss" (noun) entry of Oxford Advanced Learner's Dictionary, the verb form is listed with a hyphen. So it would be correct to write "They air-kissed.", with a hyphen.

Considering that most guides to English usage that I've checked have fully elaborated views on how to handle compound modifiers, it is quite astonishing how few of them address the question of similarly constituted compound verbs. Among the sources I consulted that had little or nothing to say on the subject are Fowler, Follett, Garner, Strunk & White, the Evanses, the Morrises, Bernstein (The Careful Writer), Warriner (English Grammar and Composition), Chicago, Words Into Type, Merriam-Webster's Dictionary of English Usage, and The Oxford Companion to the English Language.

You might suppose that the issue doesn't come up because the overwhelming majority of writers handle verb compounds such as back-form, mass-produce, plea-bargain, and right-click in the same way—which would render the OP's question about the verb form of air kiss too simple to justify extended discussion. But in my experience, the failure to take a consistent approach to hyphenating (or closing up) verb compounds of this type is one of the most common mistakes that occur in manuscripts. If everyone knows that hyphenation (or closing up) is appropriate in this situation, why do so many professional writers leave such verbs open?

I did find two books that touch on the issue. From The Columbia Guide to Standard American English (1993):

SPELLING OF COMPOUND WORDS ... Compound verbs are usually written either as single words or hyphenated: to downplay, to double-space.

From Hodges' Harbrace Handbook (11998):

Hyphens link, or make a compound of, two or more words that function as a single word... Verbs[:] He speed-read the paper. I double-checked. He hard-boiled the egg.

As the Columbia Guide suggests, the hardest question that such verbs raise tends to be whether they should be hyphenated or closed up: Should the verb form be downplay or down-play? double-space or doublespace? Whichever option you favor, you're probably not tempted leave the verb form open, as in down play and double check.

Merriam-Webster's Eleventh Collegiate Dictionary gives us these seven air-fronted verb spellings: airbrush, air-condition, air-drop, air-dry, airfreight, airlift, and airmail. The final score is Closed Up 4, Hyphenated 3, Open 0. Interestingly, whereas all four closed-up verbs follow corresponding closed-up nouns, the three hyphenated verbs are linked to one close-up noun (airdrop), one open noun (air conditioner), and one nothing at all (no noun corresponds to air-dry). On the strength of these results, and since the noun air kiss is open, I would hyphenate the verb air-kiss. I would not, in any event, leave it open as a verb.