I don't want to start a long argument but ... there really is a reason not to carry extra (and unnecessary) items on alpine climbs if you want to move fast, especially if you climb the route c2c. No matter how strong you are, every bit of extra weight slows you down. Besides, leading with an ice axe and trekking poles is not as much fun as leading light, unless you plan to use your second as a mule :))
For this climb and this time of the year, I would not be concerned about the possibility of descending snow w/o an ice axe for several reasons: 1) If you epic on East Buttress, you bail by rappelling to MR gully which is an easy descend; 2) If you need to descend from the top, you can always setup a rap; 3) the lowest summit temperatures will still be above freezing; and 4)in an unlikely event of descending frozen snow due to epic and rapid change in weather conditions, the trad gear or small sharp rocks can be used as substitutes for an ice axe.
Of course, this is just my personal opinion
