Is there any way to make my wasteland explorer switch out the outfit he's wearing?
Without recalling the explorer, no. Sometimes an explorer will change into an outfit they find, or equip a weapon they find, if it's better*, but this is fully automatic. They'll still bring back their previous equipment.
*Better doesn't always mean what you'd choose. E.g. an explorer will swap out their rusty laser (7 damage) for a 6-8 damage sawn-off shotgun they find.