Should I use a saving throw to make someone return to a cursed weapon? Details inside.

This is related to another thread I just posted but a different question. Looking for advice.

A PC got a berserker axe. After a fight with the party, the PC was knocked unconscious and relieved of the axe. The PC should want the axe back desperately. The player obviously does not.

The party plans to leave the axe behind on a remote island or drop it in the icy blue sea, and head into town to get the curse removed.

What tools can I and should I use to enforce this conflict, if any? The player will already have disadvantage with other weapons, which may be enough. But should there be a charisma saving throw that causes the player to attack anyone trying to dispose of the axe? or, alternatively to try to leave the party and return to the axe? Or even to dive into the water after it? What would you do?

The player in question is pretty non-confrontational and unmotivated so I don't expect them to rise to the roleplaying occasion.