Can I switch from one desktop wallet to another if using a cold card?
Discussion
I don't understand your question?
How do I get a different desktop wallet to pick up my cold card or something — just gift it xpub?
Why are you using your cold card with a desktop?
It's designed to work standalone. Plugging it in to a computer defeats the purpose.
Use it as signing device for PSBTs. Lots of desktop wallets support PSBTs.