I can manage to work with this library https://os.mbed.com/cookbook/ConfigFile
I just need to operate with files on the USB stick, rather than on the local flash, risking to burn it after few thousands of cycles…
The constructor of the USBMSD accept any BlockDevice so you can combinete it with any BlockDevice APIs from Storage - APIs
But from my point of view for the USB Stick you need a USBHOST library. But Mbed provide only USBDEVICE APIs.