I don't know if they have shortcuts, but if not you could likely add some automation to do it: there's Msty and ChatBox that can use any model.
I use Raycast which is a drop-in replacement for Mac spotlight along with the ChatGPT extension that lets you quickly search conversations / ask questions / etc once you provide it with your OpenAPI key.
https://github.com/raycast/extensions/tree/99c7c7c4fa02afba9...
The thing stopping me currently from trying this or Claude is I rely on the Opt+Space shortcut with the ChatGPT mac app.
Are there any other options for a native mac app with integration as good as the ChatGPT app?