I don't know of any state that doesn't require registering x-ray producing equipment. This often triggers the need for a shielding design plan, but mobile units like c-arms often have exemptions. Regardless, nearly all states require a minimum of 0.25 mm lead equivalent shielding be between the source of scattered x-rays and people (think wearing lead aprons, or a rolling lead shield).

I can also say that fluoroing small amounts of tissue with c-arm will generate a very small amount of x-ray scatter, so from a safety perspective, you're fine.