I have had good luck with TBII and TBIII for skins but have used TBIII since it came out. One thing I do is put down a thin layer of TBIII on the back of the bow, let it cure then put the skins down with TBIII. The first "sizing" gives a bit of moisture protection to the wood from the moisture in the glue and skins.
A few years ago I backed an osage recurve with snake skins and the next day I thought it had cured. I strung and shot the bow and it felt like a noodle. I let it rest for a week and it was back to it's old fighting weight. After this I started sizing the bow first before skinning and haven't had the problem since.
I believe the shellac will also seal the wood from the glue and skin moisture and the glue will stick to it.