Moisturizer sounds like a good bet. I had success using a bit of coconut oil on my Jmoney Beyer leather pads (and other leather stuff). Tropical Traditions sells an unscented and flavorless coconut oil that is cheap and great for cooking and skincare, too. http://www.tropicaltraditions.com/pure-coconut-oil.htm
Yeah there's all sorts of leather care stuff, but I figure with something that comes in contact with skin all the time, then skin lotion is a good alternative. I bought a leather jacket almost 15 years ago from Danier leather and they told me I could use hand lotion instead of their own stuff. I use whatever unscented non-fancy stuff I can find at the time and apply maybe twice a year (before and after I take it out of storage) and the leather still looks good as new.