Y doesn't contain "dick information" it contains "dick infrastructure schedule information". The infrastructure builds and maintains dickindustry.

The only thing that makes a dick and balls is a hormone signal at a specific stage in a fetus' life. Wether or not a fetus gets that signal dickindustry or pussyindustry will continue as the existing structures dictate. There are plenty of XY pussy-ovary births and XX dick-testes births due to this fact. The people usually never find out, as they lead normal lives.

Though I agree with you that her dick would show back up, that's because her regeneration is magic, not science, and the comic gods said she had a dick and that's that. It would take a big arc for her to get a pussy, old gods or time travel or dimension hopping or something.

Maybe a deal with Loki that gave wolverine a snarky, chaotic neutral pussy with its own agenda? Also, stop misgendering our beautiful wolverine!