Nope. He’s accepted his father’s sword after rejecting it twice in the movie.
Yeah, as much as I really wished we’d seen him with the green saber outside the couple flashbacks, when someone pointed this out to me on here a while back (forget who, sorry!), I finally “got” it. It should be Anakin’s saber, anything else misses the point.
Unless, I guess, you are ditching the projection angle and making Luke physically present, in which case that symbolism isn’t as important. Though then you’d have to age Mark back up to look like he does in the rest of the movie on top of rotoscoping the hilt and blade, which just seems like far too much work for so little gain over the way it is in the film itself.