I strongly suspect it will be hard to do in real-time (the information is in different systems)
That said, if you log both sets of data to the same database, you're "only" a database join (on IP address and time) away from the answer to your question.
That database join will be mildly challenging (since IP addresses can be re-used, you'll need to involve the login and disconnect messages from the WiFi auth in your database query), but it should be do-able. Once you have the time-frame and username and IP address associated together, you should be able to join on IP address and timestamp of the data logged by the SQUID proxy to associate the username with the query.
Best of luck though!