I'd take an ice axe, for sure, and maybe crampons, depending how much you want the peaks. Conditions vary greatly, from day to day. You may need an axe for getting up to Shepard Pass; many times there is a snow field covering the trail. I used crampons earlier in the year.
BTW, the class 3 section up the West Face chute route on Big Willie is only about 40 feet. One book recommends taking a rope, but I wouldn't, again. Just climb with care, or if you are a beginner, you should try easier peaks till you are good with class 3. Some 10,000' gain round trip to carry a seven pound 150m 11mm rope, if that's all you have.
And if you do do this, I'd love to see photos posted. I did both peaks slightly off-season, since I thought them too easy, then, in mid-summer.