You need something like this:
Iogear NetShair IEEE 802.11n Ethernet Wireless Router @ overstock.com
Hypothetically, with that device you could do next:
First, connect it to your pc's usb a port and configure it appropriately (for example, simple bridge between rj45 and wi-fi (bridge mode), wi-fi acting as access point, wlan authentication method, ssid, password, etc...).
Second, connect your sensor to your pc's rj45 and configure it appropriately, at least, assign it a static ip in a new subnetwork not intersected with other(s) you use.
Third, connect the configured wi-fi router to your sensor by an Ethernet cable (RJ45-RJ45) and to an external USB 5V0 power supply directly.
Fourth, find the new wlan on your pc and assign the connection with a static ip address within the same subnetwork.
Firth, work with your sensor from your pc via ip.
If your sensor has 5V0 output, or corresponding circuits onboard, you can use (but do it safely) it for powering up the router.
It's been suggested by their tech support that I use the module's RMII interface for this purpose, as I would save the hardware needed to add RJ45.
IMO, your tech support proposed you to unsolder the Ethernet PHY off the module to free RMII circuits it was connected to. I think it's not a way because you probably will not find a Wi-Fi card with RMII (they are typically designed with SDCard or PCIe interfaces) and will not re-write the module firmware to support the card (Wireless Ethernet is times complicated than its wired bro).
Therefore if you would like to solder four wires, find 5V0 and GND at the module and, if any, solder a USB A socket with a wires to them, to connect the router's usb A plug in. There are only two wires needed, even not four :) versus about ten in RMII.