Can I set another no-meeting day for secondary teams?

A no-meeting day can only be set for your primary team in Clockwise. Secondary teams will not reflect any no meeting day that has been set. It is also important to note that if a secondary team set by someone else is their primary team then Clockwise will switch it to that team as their primary. Clockwise will respect whichever primary team's no meeting day is set. 

It is possible for a company-wide no-meeting day and team no-meeting day to be set to different days, which would observe both days set. Individuals cannot disable org-wide NMDs, but can disable team no-meeting days for themselves by following these instructions.