Here's the situation, I have 2 Western Digital external hard drives
that I have plugged into my docked laptop, but this means I need to
stay docked to access those files. So, I'm looking to make those
external drives wireless so I can access the files from anywhere in
the house. I am trying to do this on the cheap with existing hardware
I own, or the cheapest additional hardware.

I have a Linksys wireless router, but it only has ethernet ports, it
does not have USB ports. I have a 4-port USB hub. What I'm thinking is
that I could plug the hard drives into the 4-port USB, and then
connect that hub to the wireless router using a USB to Ethernet
connector (which can be had for less than $20). Essentially the
connector has a USB end which I would plug into the 4-port hub, and
the other end will take an ethernet cable.

Will this actually wirelessly network the drives?

PLEASE NOTE - I do not want to consider the following options 1)
putting the drives in a NAS enclosure (since my drives are already in
their own enclosures), 2) spending $100+ on a Belkin wireless USB hub
or other similar devices.