yeah i think its 'possible' but not really . the OnInit function happens when things are loaded so you can remove it for everything, but to remove it when for speicifc items you would need to intercept the menu render process and i don't think you can (happy to be proven wrong).
what you could do, deep breath, is remove the trash entity action, and then write your own entity action to replace it, but define your own custom condition in the manifest for your trash icon, that you could then use to test if the entity action is happening on your 'sites' site, or not and remove the trash icon by failing the condition there.
you might not have to write your own trash action, you could have your own trash entity action manifest pointing back at the core trash entity, but with your own custom conditons.
so not simple. 😟