I have good experience in sending out a dweller with high S and high E stats. An outfit which pushes those values further or an outfit which will add A/L would help too.
As I noticed in my own game, people with a higher L stat often come back with more corks and more/better items. S and E will help your dweller to fight against bigger enemies.
And yes, as you already stated... a very big gun would be beneficial. ;-)
But if your dweller find a better thing on it's own - he will always equip it itself.
Another good thing are stimpacks and rad-away. I often gave them many on the road. This way they can survive for many hours. The longer the exploration - the better the loot.
I hope this helps you. :-)
Results from the wasteland are mostly random. It is highly unlikely (but not impossible, as you have the proof in your game) that a level one dweller with wimpy stats comes across the most powerful weapon in the game in an hour of exploration. Your badass explorer with top stats and elite gear might not see that type of weapon after exploring for a week. This is how the RNG works.
Because of the randomness, there is no formula that guarantees that a dweller with X stats and Y gear explore for Z time period will come back with the best loot. What we do know is that having better SPECIAL, a higher level, and exploring for longer periods of time make it more likely that the dweller finds better gear, more caps, and earns more experience than another dweller with lower stats exploring for a shorter time period finds. You can see this at work by looking at the results after multiple explorations. Jericho may not be bringing back plasma weapons and fat men every time, but he should be reliably finding shotguns, rifles, and the like rather than rusty pistols.
The other factor that you haven't mentioned with Jericho is his level. Results in my game suggest that the level of the explorer may also factor into the quality of loot they find (although part of this is that lower level wanderers just can't survive very long). My lower level explorers tend to find mostly pistols, maybe
tl;dr
Yes it's possible. Congrats on your guided fat man. With repeated expeditions, the results should be more in line of better stats + more time = better loot, but there is no surefire way of getting the absolute best loot every time. Improve your SPECIAL, improve your level, send out for as long as possible, pray to the RNGods, and send more expeditions. Eventually you will get what you are looking for.
Best Answer
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.