The Question: How to resolved this puzzle , requires an analysis of the requirements and see if it would be better to use https for whole website or a combination of http & https.
Since you are also asking for an alternative in one of your above comments, I hope the below info may help you decide on alternatives.
Background:
Basically you use http for all pages that have nothing to do with sensitive data, and https on the pages that have sensitive data.
Many times we don't prefer to use https for whole website as the data that travels is more and it takes time to encrypt and decrypt them , thereby adding up to the actual time it takes to load/display a page.
However, there are arguments against above common notion and you can also find encouragement to use https for your whole website. Check this: How to implement HTTPS only on part of website?
And, YES, secure cookies can only be used on https
pages.
Some suggestions