Remote access to data on USB flash drives?

I don't know if this is something Arduino products can do but I am hitting a wall trying to figure this out. I'll state up front that I have never used an Arduino product before but any guidance on where to start would be greatly appreciated. I need to be able to remotely pull data off of two USB flash drives that are on PCBs. They are about 20 yards apart and the WI-FI reaches fine. I need to be able to save and then delete only the data without erasing the file the data was in. We are putting in a Cradlepoint router/modem with service through AT&T with a static IP so we can access that network remotely. I have two data-loggers, separate from the flash drive that will connect to the router via WI-FI. There is a LAN port on the router that can be used. I was thinking I would plug a NAS device into the router and connect it with a USB switch to the PCB and the flash drive. The USB that is not near the router I am not sure what to do. Any help would be appreciated. Also, I only started learning about this type stuff a couple weeks ago so please take it easy on me.

Long answer short, this sort of thing I would do with a raspberry Pi.

If you google around a bit you will find tons of scripts/python code/programs that can pull this of.

Worst case scenario use a gertduino.

Good luck!

Thank you! I've been doing a bit more searching and the pi does seem better suited for this.