I have two Yongnuo Speedlite YN-568EX-II units. I can use them as radio/receivers between the two, ...
Actually, you can't. The YN-568EXII has no built-in radio capability. It can do "smart" optical slave/master, and that may be what you're thinking of, but it's a light-based system and has weaknesses of range and line-of-sight requirements. But the system will let you use TTL and HSS.
... I'm currently thinking of the Yongnuo YN-622N-TX - but is this compatible?
Not directly. You would need to add YN-622 transceivers to the feet of your YN-568EXIIs to use them with a YN-622-TX. But, basically, any TTL/HSS radio triggers made for Canon (assuming you are shooting Canon) should work with the YN-568EXII, although sometimes 3rd-party gear may not work with other 3rd party gear, the way it works with Canon gear. So sticking with Yongnuo may be your best bet. But it's not your only one.
You just have to make sure there's a dedicated transmitter/controller for the camera hotshoe, and receivers for the flash feet, and that both have all five of the contacts on the hotshoe/pins on the feet that Canon uses for camera/flash communication.
You could probably also use (among others):
- Phottix Odin II or Laso Tx/Rx sets
- PocketWizard TTL Mini and Flex
- Yongnuo YN-622/YN-622TX Yongnuo YN-E3-RT / YN-E3-RX
- Godox X1T or Xpro transmitter + X1R
- Radio Popper PX triggers
- Cactus V6II
Radio trigger technology moves swiftly, and new triggers are coming out all the time. Two of the best sites to keep up to date on what's coming out would be the Flash Havoc and Lighting Rumors blogs.
Today, most folks prefer speedlights with built-in radio triggers as being more convenient than using add-on triggers. You don't have to remember to bring along triggers and batteries for them; and if you're getting super-cheap manual-only speedlights, they often offer remote power control and possibly HSS, over manual-only speedlights without built-in triggers. The drawback, though, is that you will be tied into whatever triggering system is built in.