Well, I'd like to say rather pointedly, that drop is roughly the antithesis of the product of an atomizer, since that implies a condensed, single state of matter, whereas an atomizer disperses, or nebulizes, whatever liquid it contains.
I would say most generally, that your sentence structure being changed may open you to better options.
"Apply two squeezes of the PRODUCTNAME to your palm"
If it's truly an atomizer, and not a perfume, and you're spraying your hand with it, I have to imagine it's being used to be applied to something else or if you're testing a smaller application than the atomizer would generally administer, you could lightly touch the nozzle and squeeze, to dab yourself with the resulting drops, since they would be condensed in this case.
But for straight nouns that fit an atomizer's product, as you say spray, mist, spritz, squeeze, pump, puff (though not quite connotatively modern), squirt, application, administration, dose(though better if medicinal in some sense), cloud (a stretch), or a sample.