Hello
If I were in your place I would first do the work around.
For upgrading the DB requires downtime and it also involves many other constraints.
Also it looks like the fix was provided for the 10.2.0.4 release and most probably the latest bundle patch can have this fix included.
Again for the bundle patch installation you need a maintenance window.
I suggest you to try the work around and see if that helps.
The work around is all about recreating the synonyms and it cannot harm the system.
Regards
RB