I assume you’re focusing on Luke for this edit, so anything not involving Luke could be cut. This includes Leia’s scenes in ANH, Han and Leia in ESB, and Han, Leia, Lando in ROTJ.
ANH would work if the last we saw of Leia until the rescue was her being marched away on the Tantive.
Potential Cuts to ANH:
After crashing on Tatooine and remarking on its desolateness, Threepio could see the sandcrawler in the distance and call for help, thus skipping all of the meandering droid activity. You’d probably have to edit out the large skeleton for continuity.
To take out the Imperial Conference scene, you could hold the Homestead kitchen scene until after Ben’s Hut, so it’s Ben’s Hut - Homestead kitchen - Sandcrawler Destruction -(wipe to)- Burning Homestead -(Wipe to)- Return to Sandcrawler.
You could remove the Han/Greedo scene as well, just cut from ‘Get back to the ship, get it ready’ to ‘Okay I’ll take it’.
Taking out the destruction of Alderaan would require some tricky editing, but you could have it work by placing the chess game right after the jump to hyperspace. Then Obi-wan feels a disturbance in the Force, and Han enters the scene.
You could cut the Trash Compactor scene entirely. Just cut from Han jumping into the compactor to Obi-wan at the tractor beam control, then back to Luke and friends toweling off outside the compactor. While you’re at it, you could cut right from ‘you’re braver than I thought’ to a shortened Obi-Vader lightsaber battle, then right back to our heroes after they’ve regrouped across from the ship.
Potential cuts to ESB
Cut the Wampa cave and Han’s search for Luke. Luke is attacked and knocked off his Tauntan, but remains in the snow until Obi-wan’s Ghost shows up. Then Han shows up and in the next scene Luke is in the Bacta, presumably rescued that night. This removes the Han/Leia bickering as well.
Cut a lot of the Walker Battle. Keep it from Luke’s perspective, with minimal cutaways to other actors.
Cut the asteroids entirely. After Han discovers the Hyperdrive malfunction, he turns the ship around and immediately lands it on the back of the Star Destroyer. During this time, the two of them can share a kiss.
If you wanted to get artistic, you could show brief snippets of Han and Leia’s misadventures in Cloud City as Luke is in a Jedi Trance (3PO being blown up, Han being tortured and put in Carbon Freeze, Leia looking frightened in the direction of Darth Vader). If we weren’t shown anything about Lando or Cloud City beforehand, we are left in suspense about what is actually happening to Luke’s friends. The first time we visit Cloud City is with Luke.
Cut Yoda’s ‘There is another’ line.
Shorten Luke vs Vader by removing the bit where Vader throws things at Luke.
Potential cuts to ROTJ
Move Yoda’s death to before Tatooine. This is why Luke is taking so long to get there. His speech ends with ‘Pass on what you have learned’. Cut Obi-wan’s ghost.
Keep the Droids entering Jabba’s Palace. Chewie is already captured, as per 3PO’s dialogue. Show Leia trying to rescue Han after the droids are captured, and then Luke can arrive. Cut the Rancor scene - Jabba has decided that they will all die simply because Leia ruined his favorite decoration. Anything not directly relating to Luke is cut.
Cut Leia’s first scene with Wicket. Shorten the fire-building scene by having 3PO’s Godlike pronouncements work the first time, then cut directly to his story. Shorten Luke and Leia’s conversation.
Cut most of the ground battle and the attack on the Death Star. The focus should be on Luke vs Vader.