Mahdi Gilbert not only proves that hands, let alone hand size, don't matter, but also that innovation is going to be your best aid. Generally speaking it would be best to have the texts of the techniques you're trying to learn, and to also be willing to vary slightly from the written text and technique. I'd feel safe in saying that the books you're learning from are correct and will work for your hand size, however, the books you're studying also give you the finished version of the palm. They don't give you the gradual lessons you'd need in order to start with a passable palm and then later refine it to get the finished version of the palm. Understanding that idea will let you compromise a little while you learn and refine your palming technique.
Start with the Joe Berg Top Palm, then later you can graduate to the Updated Erdnase Top Palm. If the Joe Berg Palm is difficult to begin with, start with a Tenkai Palm or a Gambler's Flat Palm while practicing Joe Berg's Palm. Other techniques of top palms would be the Heel Clip Palm and, if you're comfortable bending cards when you palm, the Longitudinal Palm.
John Carney's handling of the Erdnase Bottom Palm would be ideal for a bottom palm, though you'll probably want to start with something like the Gambler's Cop or, better yet, Guy Hollingworth's variation on the Gambler's Cop, "The TAG Palm."
In short, you'll simply need to be versed in the various palms and know which ones work best for you. Once you've done that you'll want to start looking into things such as the framework of palming and the choreography of your routines that involve palming. Lastly, DominusDolorum's advice from Harry Lorayne on the attitude of palming is true regardless of which palm you use, so please consider it greatly as you practice.
I sincerely hope this is helpful!
Cameron J. Braxton