I don't know bbk302. It depends how comfortable you are on snow. I went without ice axe by accident as mine somehow escaped below Trail Camp. Truthfully , I did not miss it for this climb (although I do miss it for sentimental reasons as we have been through a lot together). I found crampons helpful, but honestly think that my trekking poles were more beneficial than an ice axe in these conditions. I realize that self arrest is iffy with poles, but quite frankly think that an axe would not be necessary on a fall in the chute as it isn't that steep, and would not save you falling off the crest anyway. Therefore, I did not miss it.
DISCLAIMER: My opinion only and everyone's strengths differ so others may not share that opinion. Works for me.