Finding an external wireless HDD that plex can access

Plex will run only on a full-blown NAS device.
A mere “hard drive” won’t do.

However there is no need to look explicitly for a “wireless NAS”.
Because I am pretty certain that you already have a wireless router in your home.
Simply plug in the NAS there into a free Ethernet port. If there is no free Ethernet port left, get a cheap (unmanaged) gigabit Ethernet switch to expand the number of available ports.

That being said, setting up a personal media server is probably not the ideal solution for a “casual user”. You should expect a learning curve, requiring some time and readiness to learn. Both for the NAS unit in general, and Plex in particular.