just a guess, not a real answer.
you probably need to add charle's cert in the Wii, replacing the original cert ? so charle will be able to forward requests and rewrite URLs ?
I suppose that can't be so easy.
but if eshop is closed, I'm not sure to understand why you want a SSL proxy.
if it's used to redirect to a user's repository, no need to wait for eshop to close, you could have done it anytime before.
lot of people worked on certificat issue (like Riiconnect24) to patch existing IOS and apps and still use them online after they closed their services.