Yes you can keep Cashtalk signature in your space and you can't put any hyper link or redirected link in signature.....
Even cashtalk links are hyperlinks which redirect to their website. I don't think it's acceptable. Can you confirm it with the admin? If the new rules are written by you, then no problem. If it is written by the admin, then he might have some other meaning for the first point. So better consult with him and let us know.