Those examples aren’t verbs, they’re adjectives. But the verb I’ve heard used to replace to man is to crew, as in “four men and three women crewed the space shuttle mission.”
Looking over the NASA website it looks like human is the preferred term over manned. For instance, the office in charge of putting people into space is the Human Exploration and Operations Directorate. But manned creeps into the lingo when they’re not paying attention. Manned also appears quite often in official histories with no apparent attempt to update the language of earlier eras.