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what you need is a transparent proxy. Create a separate VLAN for these users and place your proxy server in-line. You can also configure your DHCP to provide the proxy server address as default gateway on that VLAN.
You'll create a new Role that places Users from the public SSID into that VLAN.
In that scenario, all traffic from the clients will be routed through your proxy server. But you need a transparent proxy for that. If you only have a Web-Proxy for http(s) traffic than this setup might not work as expected.
hope this helps..