Nice find! I'm envious. But to haft it? That's a challenge. I've never worked with stone before.
From what I've read, some stone axes were simply used as hand axes and were never fitted with handles. Pretty hard on the fingers though.
Without drilling, I suppose the only way to attach a handle would be a compression fit. Lashings and maybe glue. Notches in the rock would help.
Fiskars basically does a compression fit with their axes, using modern fibreglass, polymers, and I assume adhesives. I have had good luck so far, but others report problems over time. There's a lot of force to absorb.
I guess the question is this: are you a purist, looking only to use materials a hunter-gatherer would have available? Wood, bone, rawhide, plant fibre cord, tendon glue, that sort of thing?
And yes, pics would be lovely.