This is an executive order, it’s not something NATCA can fight or negotiate. There is literally nothing NATCA can do other than make sure the FAA implements the EO correctly. Hell even the FAA couldn’t change this even if they wanted to.
They could voice disapproval like the postal workers union did.

APWU Statement on Mandatory Vaccination for Federal Employees
Various media outlets have reported that the White House is considering mandatory COVID-19 vaccination as a condition of employment for federal employees. Maintaining the health and safety of our members is of paramount importance. While the APWU leadership continues to encourage postal workers...

What’s the risk? Over 150 million in the us have been given the shot and a smaller percentage than people who have contracted COVID and died have got any side effects.
I think they mean the risk of contracting and dealing with Covid is a personal risk assessment, since the vast majority of people get it and recover from it with no long term issues.