This is a ski-mountaineering trip.
Weather conditions for Wednesday look good with low freezing level (2400m max in PM) and sun.

Plan A : Trying to summit wedge via the north east arete. 2200m elevation on foot (running shoes), skis and crampons. Going down the same way or via the west ridge.

Plan B : Skiing around wedge mount lake hut in case of any change in the weather/conditions.

You should : be confortable with using crampons on steep/icy snow; be fit to hike up minimum 400m elevation per hour for a long day of 12 hours; have your glacier rescue system dialed, be confortable skinning/skiing on firm pack, don't be goal oriented as conditions may change quickly in the mountains.

Gear : glacier rescue kit (+ know how to use it); 1 rope for 2 persons, avy kit, ski kit (+ ski crampons), crampons/ice axe/harnest, water/food for a long day.