I've done it a few times, sometimes with no axe at all, sometimes with a general axe, and once with one technical tool (simply because I was ice climbing on that trip and didn't want to carry two kinds of axe to my campsite).
I've heard of people using a rope on the steep step near the bottom of the route, but it's totally unnecessary. There are tons of handholds. I do recommend you put on crampons before climbing that step, as the step is difficult to climb in snowshoes and the next section is shaded and tends to be very icy.
The route is the kind where if you've got an axe and want to practice using it, you'll be happy to bring it. (Please refrain from hooking roots or branches - it damages them.) It's not entirely necessary in most conditions, but nice to have along in case of unusually slippery conditions. Carrying two axes is extreme overkill.