Actually, there's probably a sufficient amount of evidence that a lawyer will take it pro-bono
I suspect you meant "No win, no fee" Will lawyers do that in contract disputes?
Given that CC probably have more money to spend on a court case than OP, is there not a danger of them just outlasting OP? Even if a lawyer is willing to wait for their fee, I think OP would have to pay all expenses on an ongoing basis. I think the OP team would have to be pretty certain of collecting a large amount of damages in order to even consider it. I'd be worried about the costs potentially dragging down the company.