Have you looked at Lightning or Wifi compatible USB drives? I don't have any experience with these things and it seems that most have been designed to extend the storage of an iPad or iPhone, but depending on the apps one or more might fit the bill here.
Best external storage drives & accessories for iPhone & iPad 2017 - Macworld UK
There are some other articles about this subject if you Google 'usb stick with lightning connector' but the link above is the most recent one.