In my small company (15 machines), we currently have a router which has the WAN connection. A switch is then connected to this router. And all other machines are wired to this switch. It works fine.
Now, this router with WAN connection may be taken away, and would be replaced with a wireless access point only. No way to plug a cable going to the switch then.
The goal is to keep sharing internet access to all existing machines.
I thought about using a Wi-Fi range extender which has an ethernet port, configure it to client mode and wire the switch there. But in all user manuals I've seen, only one device is shown as wired in this mode. I also couldn't find a wireless access point with client mode supporting up to 15 devices and maybe more in the future.
Buying a Wi-Fi USB adapter for each machine would work, but then I'd have to use Wi-Fi range extenders for the farthest devices, and the currently used switch + cables would be useless.
What would be the best way to share a main wireless connection to all currently wired machines?
Edit: add small architecture for clarification