To make this change work you have to replace Ankin’s saber with Luke’s throughout TFA and TLJ.
No you don’t. Why would you?
If the whole idea is that Luke’s legend as a Jedi grew in the years after ROTJ, most people would be familiar with his green lightsaber anyway (he’s had that for 3 decades compared to a couple years with the blue one), so it makes more sense (to me) for his projection to use his green one rather than Anakin’s blue one.
In TFA and TLJ, his blue lightsaber represents the lost myth of Luke Skywalker and the Jedi that they need to find and bring back.
At the end of TFA and the beginning of TLJ, Rey offers Luke the lightsaber, in essence asking for his help to come back and save the galaxy. Luke refuses by walking away. Later, when Rey says that she’s going to go to Ben and Luke says don’t, she offers the saber once again, and he says no. So she has no choice but to got to Ben.
During the course of Rey and Ben’s interaction, she gives him the saber (albeit in a non-traditional way). She thinks he’s the person who will save the galaxy. But when she learns he wants to destroy the Resistance still, she tries to take the saber back. She can’t it breaks in two, and it seems she’s stuck, hopeless.
But then Luke shows up! He’s finally accepted Rey’s offer, he’s come back to face down the First Order and save the Resistance. So what lightsaber should he be using? The one Rey offered him.
At the end, Luke is dead and Rey is left with the broken saber. She asks Leia, despairing, “how can we build a rebellion from this?” Leia takes her hand that’s holding the saber and says “We have everything we need.” The clear implication: they’ll rebuild the rebellion, obviously, but also the Jedi and (potentially) the saber too.