The only way to achieve this would be:
_Making Anakin force grab one of Grievous Red Lightsabers (wich will be Darth Vader's lightsaber) by mistake.
_Changing the shot of Obi-Wan grabing the lightsaber from the floor of Mustafar to the floor of the Utapau landing platform. Since they dont see each other again, there is no way he can give it back.
BAD THINGS_
_It seems forced and convinient
_It makes the situation of lightsabers a bit confusing because Obi-Wan just lost his... It would be: Obi Wan looses his lightsaber, picks up Anakin lightsaber, and then he picks his back again.
_Why wouldnt Obi-Wan or Grievous use Anakin's lightsaber during the whole fight.
_Since the red lightsaber is a symbol of the dark side, feels like Anakin turns to the dark side by mistake.
_The lightsaber hilt will still be Anakins, not Vaders.
GOOD THINGS_
_Anakin will have blue and red before killing Dooku, and just after THAT he will only use red lightsaber (pretty symbolic too)
_Anakin will use a red lightsaber to kill Mace Windu
_You wont need Anakin manufacturing a red lightsaber for the final Mustafar battle.