It really doesn't make sense that anyone on the ship would wake up with gear at all. After searching around the ship we should find some basic stuff to get through the first fight, then in the next area we should be able to find more through scavenging or maybe a "prisoner chest". These would contain all types of generic weapons and armour so we could properly equip before the final room. Lae'zel and Shadowheart should not have custom gear at all, instead specialty gear should be able to be looted in the appropriate areas with a crafting option given as well, maybe this unlocks once we pick up a particular style.