A switch does not need an IP address to operate at layer 2 as your message shows this switch has been in place for a while and is switching frames. You do need an IP address to manage the switch and to access it remotely. As far as I know without an IP address assigned it is not possible to access the switch remotely. The access to a switch which does not have an IP address is through its console port.
There may be one possibility of a way to work around this. If someone can connect the console port of the switch and the AUX port of the router, you may be able to do a reverse telnet through the AUX port of the router to the switch. If that works you can configure an IP address on the switch through the reverse telnet. Otherwise I believe that someone with a PC will have to go to the switch, physically connect to the console port and make the config change.
That's kind of what I figured. The switch and router are not close enough to eachother for a rollover cable for reverse telnet (router and switch are in different rooms), looks like a road trip for me!
it will be a road trip for u and in future keep it in mind that if you don't want to give in the IP initially to the switch never forget to connect the console port of the switch to the aux port of the router and make the reserve telnet config on switch also.