Replacing the Ethernet Shield with a WiFi shield will require some adaptions to the ArdOSC library. The ArdOSC library contains a few function calls to the lower level SPI functions of the Ethernet library.
I personally am not working with the ArdOSC library anymore as it is rather dated and not maintained anymore. I have rewritten my code to use the OSC library from CNMAT (Oscuino) GitHub - CNMAT/OSC: OSC: Arduino and Teensy implementation of OSC encoding. It is writen and maintained by the inventors of the OSC protocol and actively maintained.
It uses the "regular" Arduino Ethernet and EthernetUDP libraries and is not directly hardware dependent. However, using hardware that can make direct use of the the Arduino Ethernet libraries is a not to be underestimated advantage to getting things to work very quickly.
For example I use a WIZ820io Ethernet module instead of the Ethernet Shield.
Any change in Ethernet related hardware will require you to change code in the used libraries unless the libraries that come with these shields e.g. the Seedstudio WiFi shield have compatible function calls.