For those who are interested, there is a solution for having both Wifi and external microSD storage on the OAK-D-CM4 PoE board.
This forum post on the raspberry pi forums contains some details on how to create a new pin overlay, compile it, and add it to the boot config. This has worked for me - both the Wifi and external SD card are functional - though I don't see it being widely useful, since you need a PoE connection to power the device anyway.
In my use-case, connecting to the camera while on-site is difficult, as the wired network is managed by another party. I have access from the internet to a virtual machine on the wired network from which I can access the camera, but the site has very bad mobile reception, so this solution is patchy if it works at all. Setting up the pi as a wifi access point allows me to directly connect when physically next to the camera.