I would suggest bringing the rope, tech gear, boots, crampons, & ice axe. If conditions aren't suitable for the Sunshine Peewee route (east buttress), you can always give the mountaineer's route a go. I climbed the whole route (including leading the crux) in May a number of years ago in La Sportiva Nepals- I'd recommend doing it with boots, if you're comfortable with it- it will likely be cold. Also bear in mind that the route is fairly sustained mid 5th, & the crux is somewhat poorly protected (bring nuts, small cams, & maybe a Screamer or 2); you could maybe switch into rock shoes for this (rest of the route's other cruxes are well protected). Also, don't underestimate the descent (i.e. the mountaineer's route), esp. if you haven't been on it before- it is non-trivial (esp. in the ice/snow), requires care & time while downclimbing, & glissading should NOT be attempted- a number of people have had fatal accidents. Know the turnoff that gets you down to Iceberg Lake, too. Make sure your food is safe while you're going up the mountain- I'd thought my food would be safe hanging it from one of the small, last trees found right below Upper Boyscout, as everything was snow-covered- I returned to find the majority of it ravaged by a hungry rodent.
Good luck, be safe, & have fun!