Do you run the cache / contract with someone to run the cache, or are you worried about third parties who run caching servers out of your control (like mobile ISPs, corporate networks, etc.)? If the latter, I'm surprised/curious what the use case is.

If the former, you can stick those on HTTPS too just fine. CloudFlare will be an entire SSL-enabled CDN for you for free. Amazon Cloudfront will serve SSL for you for free (though you still have to pay for Cloudfront itself, and get a cert on your own, though you can do that for free).