OK. I'm getting confused by all the saber switcheroo.
The saber you've shown in Palpatine's desk is Vader's black & silver saber. This is a different saber from Anakin's silver saber that is later given to Luke (which Anakin has just used to lop off Windu's arm).
So if you're fixing this in ANH, that implies to me that Luke will receive the black & silver saber. But he obviously receives the silver one. So, yeah, I'm confused.