I'm catching up on my reading today while killing time in a hotel room, and
just read a recently-published study that helps to answer this question
(unfortunately not open access): Ivana Papežíková, et al (2017) Effect of
oxalic acid on the mite Varroa destructor and its host the honey bee Apis
mellifera.

In their well-designed and executed experiments, they demonstrated that
varroa dies fairly quickly after even brief exposure to vapor-produced fine
OA crystals, and that the mites don't avoid exposure to the crystals.

There was no effect on mites from vaporization of OA once it had
recrystallized--the mites must contact the crystals.

Of even more interest is that mites suffered the highest mortality after
feeding on bees that had consumed OA in syrup (I wouldn't be surprised if
we find that they also consume some when grooming themselves).  The
mortality of mites was substantially higher for those placed on bees that
had directly consumed dribble syrup than for those on bees that had been
trickled or vaporized.

They found that vaporized OA may have had a statistically-insignificant
lesser adverse effect upon the bees than did trickling.

-- 
Randy Oliver
Grass Valley, CA
www.ScientificBeekeeping.com

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