26650's have more capacity and are normally rated for higher current. You won't need the higher current rating of most 26650 batteries compared to many of the 18650's anyway which can have plenty, but I prefer them because under a heavy load their peak voltage doesn't sag as quickly. Are they really needed? Unless you have some bad or low current 18650's probably a waste of money if you can make do with those, but there is no way I would run this diode on less than the 26650's myself, I like the extra capacity and their ability to pull large amounts of current without their voltage draining down as fast.
So, my advice is, get a host which can hold 26650's, I don't think you will regret it unless you just don't like the larger diameter. Much depends upon how you operate the laser, for short duty cycles, which you will likely be force to use anyway unless you have a very good heat sink, it won't make any difference.