Other federal workers. Some federal employees work on projects and programs funded with money other than annual appropriations. These workers likely will continue to be paid on time throughout the shutdown.
Supreme Court Justices. There is a constitutional prohibition against a "diminution" in pay for the justices so, like Trump and members of Congress, they will continue to be paid on time throughout the shutdown.
One of the main reasons for this is that unless specifically authorized by law, no one is allowed to volunteer for a federal agency. However, federal employees' paychecks for time worked during the shutdown may be delayed until the shutdown ends.