We might start an inquiry in the women's forum: "does any girl "go commando" in Kendo?" ("freeballing" for a girl what could be used?)
I usually wear running shorts under my hakama because I like to be able to whip my hakama off and pack up without having to go into the bathroom and change. Also, I find that it soaks up the sweat so I don't have it dripping down my legs making the floor all slippery. I sweat so much during keiko that my keikogi doesn't catch it all. What kind of running shorts are you wearing? I usually wear the type with the slit up the side. I think this link will work. Or I wear this with nylon panties underneath. As for the commando question... the closest I've gone to that is wearing nothing but a g-string (didn't have time to change after work). It was very uncomfortable. I did not like the feel of the keikogi on my bare cheeks or well... let's just say sonkyo really sucked that day.