If you block ALL outgoing access to the internet for port 80, 443 (http, https) and ONLY allow access through the proxy they cannot pass the internet access controls...
the other route could be to install a transparent proxy, that silently routes ALL traffic through a proxy.
http://www.cyberciti.biz/tips/linux-setup-transparent-proxy-squid-howto.htmlin the latter case there is no need to configure a proxy. For a transparant proxy you only need an extra system with two ethernet interfaces sitting between your network and the outside, it can also be configured to be run like a bridge (network switch like).