I don't think you'll have enough pressure for misting from a small pump, and even so, the misters would clog unless you used distilled or spring water. Also, a constant mist is not desirable, as the plants may rot. Why not just do a drip wall using the same principles you mentioned? (don't wrap the pump in batting.) You could use either some regular tubing punched full of holes and sealed with silicon on the end, or use an adaptor to hook the tubing from the pump to the garden soaker type tubing. Run this across the top of a background of cork bark, a tree fern fiber slab, or a piece of CocoTek grow slab, and let the water trickle down through this. (You can also plant these drip backgrounds with moss, vines, etc.) This will cut down on hand misting a great deal, if not entirely. The tub with holes in it would need to be in a false bottom, of course, so there is complete circulation.
What I've been doing for a false bottom recently, is using the Coco-Tek grow slabs to support the substrate, with a layer of weed cloth on top to filter out the fine particles. Then I just cut out a section for the pump, hide it with a pile of aquarium rock or gravel, and cut out any ponds I want. The Coco-Tek slabs are about 3" thick and come in sections of 6"X3"X36", but they can be easily split lengthwise for thinner sections, or to layer up for a deeper false bottom. One nice feature, is the frogs cannot possible get into a pond and inadvertently get trapped in the false bottom. The slabs are loosely woven cocoanut fiber, which is sturdied up I believe with latex so they don't deteriorate.
Black Jungle carries the tree fern panels, and the "Cork Store" has cork bark either in bulk or individual pieces. The above two are easy to look up, but I'm adding a link to the Coco-slabs, because they are hard to find on a search.
I've become a big fan of drip walls, and have used all three media for them that I mentioned above. Most all of the tanks I have these in rarely if ever require misting, and the frogs love it.
I just use 1 gallon pump mixers available at any nursery with spring water, which is really no trouble, especially if you don't have to use them very often.
Link
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Patty
Pahsimeroi, Idaho
4 D. auratus blue
5 D. galactonotus pumpkin orange splash back
7 D. imitator
6 D. leucomelas
4 D. pumilio Bastimentos
4 D. fantasticus
6 P. terribilis mint and organe
4 D. reticulatus
4 D. castaneoticus
2 D. azureus
4 P vittatus
2 P. lugubris