Need External Drive

I am looking for a wireless external hard drive (about 4TB) to put my videos on. This will be hooked up to my MacBook Pro. I don't want one that emits its own Wifi which would make it so that my laptop has to connect to the drive's Wifi and, therefore, can't connect to my home Wifi at the same time.

I want the external drive to be also backed up on my online backup service so I want it to mount as an additional drive. Also has to be Mac compatible (though not Time Machine, I won't use that).

My husband tells me that I can't hook up a USB external drive to our router because it's Windows based, and I need the external drive to be formatted for a Mac.

Are the only Wireless type external hard drives WiFi? Is there a difference or not? I don't want to use USB because I'm trying to avoid cluttering cables all over the place.

I don't want a drive that I'll be taking with me anywhere so I can access my videos.. I don't want it to backup my tablet or my phone. Just videos on my MacBook Pro.

Thanks!