Two ideas:
Some WiFi SD cards (normally used by photographers to transfer photos while they are shooting, e.g. to get "live" updates during an event out to social media) have a hackable Linux on them, which you probably could modify to fetch images from the outside. The target device would have to understand an SD card in a USB reader as a storage device, but many should.
RaspberryPi Zero can do some USB client functionality, you could check out what's already been done there.