Congrats on getting a running watch !
I’ve seen this a few times, where someone doesn’t realize that you have to wear an “automatic” to keep it running.
Most split stems will simply pull apart with enough pressure.
A hand remover will work sometimes, but they sell a crown remover as well, which is a bit more “robust”, and they are worth the money in my opinion.
I am not real familiar with the Omega Connies and the crown set-up, so I would find someone else to verify that a crown remover is the preferred tool.
Bob will probably know, or someone in one of the Omega forums online.
If it will pull apart, you always risk that one of the pieces can break, just from age/fatigue.
Best of luck
Randy