I’m not a lawyer and I’ll accept you’re correct. The only comment I can add is that even if no injunction is in place while this case is retried on the district level, is that the regulation is widely and almost entirely ignored as virtually no mpb mohelim in NYC are using the form and it is entirely unenforceable from a practical standpoint. This will remain so even if the regulation is ultimately upheld. The city knows it isn’t going to be placing NYPD officers in every Orthodox shul across the five boroughs to witness whether mbp is performed and record whether a form was signed or not.
Also, the DOH regulation was issued in the same legal format as the DOH issues restaurant violation notices. Even had it been enforceable, the most the DOH could do is issue a fine. From a legal perspective it is like a civil parking ticket and failure to provide the consent form is not a crime. And whereas the DOH can shut down a restaurant for multiple violations, the DOH is legally powerless to stop a mohel from continuing to engage is a religious ritual.