As long as you aren't using any apps that verify both ends of the cert communication
Apps like this probably don't work over an ordinary HTTP proxy anyway. Nor do they typically need caching, so you could probably just run them straight out to the Internet.
as long as you don't care or need to see whether certs have EV
Then have the proxy verify the EV and use a separate EV certificate (which you have accepted in your browser)
especially when working in some industries where SSL inspection of various classes of traffic can be illegal due to breach's of various privacy and confidentiality laws
If deep inspecting HTTPS for the sole purpose of office-wide caching is illegal, then deep inspecting HTTP ought to be illegal too.