Wireless :: Using Two Browsers To Connect Via Lan And Tethered Wifi?

I work at a client site which lets contractors connect via a proxy Ethernet connection. A lot of URLs (e. g. webmail) are blocked though for security reasons. The rest of the time I switch over to a tethered 4G connection, having to change the proxy configuration in my browser(s). I use both IE and Firefox. I know that the laptop connects to both networks simultaneously, but the Ethernet connection is given priority when connected. Is there a way to have say my Firefox browser configured to use the tethered connection using no proxy, while simultaneously having my IE use the Ethernet connection with the proxy configuration?