Desperation knows no limits.
He could also act in the medical area via administrative law by requiring providers to ask about gun ownership. In fact, the crappy Wisconsin Medical Society which is branch of the equally crappy AMA looks favorably on gun restrictions.
We should also be aware that DSM5 has a diagnosis of oppositional defiance disorder (basically those opposing authority figures) that could be used against many here on FR.
The state department of health services also runs the controlled substances database so they can know who takes amphetamines, opioids, benzos. We know that law enforcement can troll through this.
They can also require that sales of guns and ammo are with digital currency and not cash. They already have precedent with state law here. However, this would probably need legislation.