If you can't allow SSL on your network, you can't allow use of Google and about 2000 sites which browsers will not even try opening via HTTP:
https://code.google.com/p/chromium/codesearch#chromium/src/n...
Jail libraries and magic-cookie-hunting hackers have an option of installing their own CA certificate. This is supported by all browsers. It's not hard, even Lenovo malware can do it.