add a router, still use wireless
There are lots of terrible ways to do this, like buying a wireless access point and asking it to be a client to your current wireless router, or bridge to it, and then run a wired network from that which falls in the same broadcast domain as your wireless network ... or set up a wired network with a different IP range than your wireless network, but no default gateway, so default gateway (internet) communication still goes through the wireless even though it would generally not be the preferred route.
I think the real solution is to have a router. You can keep your old wireless connection to your internet router if you like to, or need to, fine. But the mac mini, or some other dedicated device, should provide its own network with DNS, DHCP, NAT, and uplink to your wireless network. Now you can add a wireless access point to your new downstream network and have the wireless uplink to the internet, and a proper hybrid wired and wireless infrastructure in your office that you can hop between wired and wireless seamlessly without dropping connectivity. The internet will have some additional difficulty getting to you because you're now behind another NAT, but you can get out just fine. It's like another firewall.
inet - modem - wifi - mac mini as router - gbit switch - {WAP, wired clients}
If you don't add the additional Wireless AP, then wireless client won't be able to access wired clients, but wired clients would be able to access wireless clients.
With the additional router scenario, you can place it in an optimal location to contact either the current router, or the wireless clients and old router, maximizing throughput.
Though this really does sound like you're just being cheap, and the proper network I described is a little painful to setup and maintain. That's why you're getting such push-back on just getting a proper router.
