Safe method to reset SQL system related passwords without service disruption

Is there a safe way to change the passwords for these SQL users without disrupting the system?
mysql
postfix
root
roundcube

I can see that all of them (except roundcube) have their own Linux user accounts, but it seems they don’t have passwords set. So I assume changing (or adding) the system password won’t have much effect.

I could use phpMyAdmin to change their passwords, but that might risk disabling services I rely on.
I see that I'm able to change these passwords by the admin panel, but I'm afraid to do it without knowing how it will end up! Is it safe for these users to change their password?

Is there an internal script available to safely reset these passwords?