Opinions on this Theorycrafted Corki Build

The Sorcerer's Shoes boost his ultimate, Q, and W damage so of course I would get them. A Trinity Force is a must on Corki. The next two items are what I'm actually wondering about. Sterak's Gage to boost Trinity Force damage and give Corki tons of defensive stats. Rylai's boosts Corki's damage a good bit actually and gives him even more health to work with. It also gives his ult and his E a good 40% constant slow to kite with. Statikk and Infinity Edge are there to help Corki's sustained damage and make his Trinity burst a lot more potentially. Thoughts? Could this be a good build? I feel like I might need to trade Statikk for a life steal item.