Can I choose a specific (at least not Turing) hub for my Binder links?

Please read here and here. Why this is only encouraged as a temporary workaround and examples of how are included there.

Links are covered above in the first part of this reply.
Please examine how the badge links work. They are just markdown or restructured formatted hyperlinks. You should then see how you can change the text for the badges to point wherever you want.