“Green Lantern? Funny name for a perceptive cop who has never-back-down willpower and comes from Philadelphia. What do they call you up there?”
“THEY CALL ME MISTER TIBBS!”
I had a tab open on this guy before opening this thread, I’m not sure about the other requirements but you have to admit he would use the ring in pretty imaginative ways 
That’s certainly a cross-over I’d like to see 
I may be wrong but Conan never struck me as particularly imaginative, wouldn’t he try to solve all his problems by just creating a really large green sword?
Not sure how imaginative he’d be about it, but problems tend to just sort of go away near a calm guy who has a Medal of Honor and goes by the name of Miyagi.
Longfellow Deeds (original, not remake) and Jefferson Smith come to mind for some reason…
Imagination has never been a huge deal for Lanterns. Most of them - Hal, Guy, a bunch of the aliens - basically have a handful of go-to constructs which are things familiar to them - military hardware, baseball gloves and bats, boxing gloves, that sort of thing - and even Kyle or John usually solve things by making constructs to hit or shoot the bad guys.
Conan would be out of his element if something like a complex truss was needed, or if someone needed microsurgery, but the same would be true of Hal, or Guy, or even Kyle.
When I considered real-world candidates, I was at once struck by the idea of Stephen Hawking wielding a ring.
Well my only experience of the GL story universe is the DC animated TV series Justice League and the movie where its repeatedly stated that the only limit to the power of the ring is the imagination of the person wielding it. It seems kind of a loss if its only used to make things like that, though I certainly understand why its depicted that way. 
Like Conan’s sword, a GL Hawking would probably just solve everything with artificially created black holes 
(Can the ring do that? Could it heal his illness and body as well?)
I could give it a shot.
I remember when I was in high school, in shop class, I made a ceramic elephant that was also a lamp (when you pulled on the elephant’s trunk, the light came on). So, given the right materials (and a can of green spray paint), I could probably manage it.
Ryan Reynolds.
A young Michael Douglas would make a fine Hal Jordan.
Imagine Plastic Man with a Ring.
They once did a TV series where the entire point was that folks were trying to get our hero to crack: they’d pump him full of drugs to shoot for Pavlovian effects with electric shocks, and pump him full of drugs before making him dazedly playact his way through life-and-death events, and pump him full of drugs before making sure the guy caught a beating, and pump him full of drugs — you know what? Let’s just say he struggled to keep it together, and despite the drugs in his system he somehow kept managing to insist that he is not a number; he is a free man.