Antonia, sorry to hear about the cat. That's no fun but you don't want them suffering either. I don't envy the choice.
As for your ex? I see no reason to tell him based on what you say. I think this is a test for you to do this on your own.
Just my thoughts. Sorry it has to be done.
AJ
"Our lives begin to end the day we become silent about things that matter" MLK Put the glass down... "Yesterday I was clever so I wanted to change the world Today I am wise, so I am changing myself."