It depends on how much control they have over the end points - if they control the end points they could potentially force the proxy config. If they want to block for any random end point then you would block all ports on the router and only allow outbound via the proxy.
However, thinking further to do application level blocking on 443 would also require a firewall that is capable of SSL interception and inspection. Not sure how capable squid is but they could be looking at enterprise grade firewall/proxy to enable all of this.
EDIT : looks like squid can do SSL interception using
SSL Bump. However, might require quite a bit of research on the OPs part to work out how to get all of this working properly - it is unlikely to be for the faint hearted.
Edited by ian72 (Thu 06-Feb-20 10:59:51)