Applying a skin to a foam wing is a chore. I have used 77, epoxy, and a couple other items. My favorite one that I settled on some 25 +/- years ago is to use one of the off-white carpenter's glue thinned 50-50/60-40 or about, with water. Now this takes a lot of time so if in a hurry, forget it. It has worked well with balsa skins and 1/64 plywood.
Once you are ready, with thinned glue, brush on a coat on both the foam and the mating wood side. Press together, do both wing sides and place back into the foam blocks from which the core came. When all is aligned as you want, apply a LOT of weight. Old magazines are very good as the weight can be fairly evenly spread.
Now tend to business for a week. Remove the weights and the foam outer blocks. BE STRONG as you will think the wood is rotten. After a day or so out, the wood will dry out and look much better. Then back into the foam blocks and go about your business for another week. Again remove and let dry for a couple days then finish as you so desire. If this is a serious project, finish painting can be expedited by an application of thinned finishing resin, epoxy easier and less smelly, but polyester works well and sands easier. You have a nice base to finish, and the wood will not separate from the foam or at least it never has for me.
Just the other day, I was looking at an old model in the barn that is some 20+ years old. A good hard finish (polyurethane) is still there and no pop-ups (this one is 1/64 ply). The barn has no airconditioning and everything there is subject to the heat, humidity and cold of the South East TX climate.
It is a good procedure, however the long drying is IMO what makes said procedure work so very well.