The Soundstyle Z2 stands appear to have a top plate that is 5"W X 6.5"D and a base that is 8.9"W X 12"D. The Aviano 1 is 7.2"W X 10.7"D. It's a good idea if possible to have a top plate at least as big as the speaker's base, but that's not the case with this pairing.
Some people have luck with using Blu-Tak putty to affix the speaker to the top plate, but I'm not sure that would hold against a heavy leaping tomcat. The better solution would be to install one or two threaded inserts into the bottom of the speaker and drill a hole through the stand top plate for a bolt(s). One method is to install a flanged insert from inside the speaker (woofer removal required) and the other would be to install a double-threaded insert (that have internal machine threads and outside wood threads) into the bottom of the speaker from the outside, which threads into the wood of the cabinet.
The remaining vulnerability would be if such a leap from your cat would be able to topple the entire speaker and stand. If so, fastening the base to either a larger bottom plate or attaching larger "outriggers" would be a solution.
I wouldn't worry too much about the damage to the speaker, if it seems to sound OK, then it is probably just cosmetic. If you're uncertain, you can always carefully compare it to the unfallen speaker.
Steve