Setup the Cron that you made:
“At 09:30:00am, on the nearest weekday to the 1st of the month, every month”
(Keeping is simple for now)
Could you not setup the Cron without a calendar associated? Or does it need to not run on Public Holidays? If so, you could manually review the next 12 months and then setup one time triggers for that date or manually run them the next day?
Another option, bit more complex though, you could setup a separate calendar and have it run on the first two days of the month. Then use a separate calendar to make it only run on the day you need it.
Probably some better suggestions out there from the community