I remember the Dolphin Team consulted with a lawyer who said they don't need to worry about any legal danger because of 17 U.S.C. § 1201(f)(2), which states:
"...a person may develop and employ technological means to circumvent a technological measure, or to circumvent protection afforded by a technological measure, in order to enable the identification and analysis under paragraph (1), or for the purpose of enabling interoperability of an independently created computer program with other programs, if such means are necessary to achieve such interoperability, to the extent that doing so does not constitute infringement under this title."
And 17 U.S.C. § 1201(f)(3) says:
"The information acquired through the acts permitted under paragraph (1), and the means permitted under paragraph (2), may be made available to others if the person referred to in paragraph (1) or (2), as the case may be, provides such information or means solely for the purpose of enabling interoperability of an independently created computer program with other programs, and to the extent that doing so does not constitute infringement under this title or violate applicable law other than this section."
Which means that Dolphin could likely be engaging in fair use by utilizing the encryption keys. If Dolphin was really worried about legal danger, they would have removed the keys and made it so you have to find the key yourself. But they didn't because it's basically a non-issue. The Wii Common Key has been all over the internet for over 15 years now. We all know this, even Nintendo knows it. They just didn't do anything about it until last year because they didn't want it on the Steam Store. After they cancelled the Steam release, Nintendo left Dolphin alone. And IIRC Nintendo hired some people who worked on Dolphin to help develop the official Wii emulator for Nvidia Shield.