How can I use a WeMo controller on a non-standard outlet?
Adapting a 120V controller for a 240V (208 is unlikely unless you have 3-phase power) plug seems remarkably foolish... 

Quoting wikipedia: "NEMA 6 devices, while specified as 250 V, may be used for either 208 V or 240 V circuits, generally depending on whether the building has a three-phase or split-phase power supply, respectively." 

To Quote Belkin, Wemo ratings: "Max 120V~/16A/60Hz/1800W" 

Either educate yourself far enough to use a 240V relay with a 120V coil to control the A/C (plug the COIL into the WeMo) or forget this as baaaaaaad idea.