disclaimer: I am not a lawyer.
In short, no. You're not required to share anything when you use or adapt CC content.
So, while you may share your final product, you aren't required to share the intermediate forms, including source code.
Quoting from the CC-BY-SA 4.0 license (paraphrased and emphasis added):
Section 3.a. (Attribution) says "If You Share ...
What would be a suitable license for this situation?
The license that comes closest to your desires seems to be the Apache 2.0 license.
It is a permissive license that allows derived works to be distributed under different terms than your template and it has a mechanism for handling attribution notices. The license does have a requirement that if different ...