Regularjoe gave me an idea. It would be pretty easy to remove all mention of Leia as Luke's sister from the movie, starting with the Ben scene:

"the other he spoke of is your twin sister."

"But I have no sister."

"To protect you both from the Emperor, you were hidden from your father when you were born. The Emperor knew, as I did, if Anakin were to have any offspring, they would be a threat to him. That is the reason that your sister remains safely anonymous."

Ben does not continue, and Luke processes this new information, then looks at Ben (from the final shot in the scene).

Ben continues: "Bury your feelings deep down, Luke. They do you credit, but they could be made to serve the Emperor."

Ben could be fading out throughout this scene, and his last line is only a voice in Luke's mind.

Then of course the talk of Leia as his sister is taken out of the Ewok village dialogue, and the throne room scene can stay as is. Leia's talk with Han goes somewhat differently:

"You love him. Don't you?"

"It's not like that at all!"

This would require some careful cutting to feel genuine.

Or, it could be made to seem like Luke doesn't know who his sister is, and during the Ewok Village dialogue, he suspects that Leia may be his sister. However, he omits telling Leia about his suspicions.

It goes as in the movie until:

"He's my father."

"Your father?"

"There's more. The only hope for the Alliance, if I don't make it back..."

"Luke, don't talk that way."

"It won't be easy for you to hear it, but you must. The Force is strong in my family. My father has it. I have it. My sister has it. In time, my sister'll learn to use that power as I have."

"Then Luke, run away, far away. If he can feel your presence, then leave this place! I wish I could go with you."

"No you don't. You've always been strong."

"But why must you confront him?"

"Because there is good in him, I've felt it. He won't turn me over to the Emperor, I can save him. I can turn him back...(Leia stares at him)...I have to try."