Assuming USA:

The software can absolutely be declared illegal under DMCA and has already been done to the DVD decrytion software DeCSS. Nintendo would just have to convince the courts that the primary purpose of the software is to circumvent their DRM, and I doubt any lawyer would want to defend that when circumventing copy protection is absolutely happening.

Relevant DMCA passage:

Section 1201(a)(2) of the Copyright Act, part of the DMCA, provides that:

"No person shall . . . offer to the public, provide or otherwise traffic in any technology . . . that—

"(A) is primarily designed or produced for the purpose of circumventing a technological measure that effectively controls access to a work protected under [the Copyright Act];

"(B) has only limited commercially significant purpose or use other than to circumvent a technological measure that effectively controls access to a work protected under [the Copyright Act]; or

“(C) is marketed by that person or another acting in concert with that person with that person’s knowledge for use in circumventing a technological measure that effectively controls access to a work protected under [the Copyright Act].”

The injunction that was granted: https://cryptome.org/dvd-mpaa-3-pi.htm

Court’s findings and arguments for granting the injunction: https://cyber.harvard.edu/openlaw/DVD/filings/NY/0202-mem-order.html

See also: https://en.wikipedia.org/wiki/Illegal_number

Nintendo’s legal argument is that the encryption that is reverse-engineered to circumvent copy-protection is protected intellectual property.

Anyone can copy the contents of a switch ROM (more of a glorified SD card anyway) but the million-dollar question is whether their proprietary encryption can be broken legally.