I think you need to clarify your thinking because your question doesn't really make sense.
Static and secure are not mutually exclusive or even related to each other. You can have secure static content and non-secure non-static content. Secure just means it's encrypted (SSL, i.e., https). Static means it's not generated per-request for the client. These are two fundamentally different concepts.
If you're not mixing up your terminology, then I would ask why your secure server can't serve static content. My guess is that it does, so you just need to put your static content onto the secure server and then a browser won't complain about the mixed http/https content because it will all be https. If there is truly some technical limitation on the secure server that prevents it from serving static content (e.g., it can't even serve a CSS file), then yes, you should look at adding SSL to the other server you're using.