Thanks, but I’m just another customer. This forum was set up several years ago so that customers could help other customers with ideas and is information. It’s only monitored by SmartThings staff for issues like harassment and spam. So I’m just paying it forward: lots of people here have helped me in the past.
As far as a no neutral option for controlling a receptacle, I don’t know of one for North American homes. There are a couple that are designed for Asian homes, which have a different electrical system, lower loads, and don’t have the same required safety certifications.
But as others suggested here, there’s definitely a neutral somewhere, the outlet itself needs it. The switch is just a cut out in the line, but that’s not the only thing. So you should be able to put an in wall relay somewhere along the circuit that would work to control the outlet. (Or replace the outlet with a smart outlet)
And then you could replace the existing dumb wall switch with any smart device you want, but take it out of the circuit to the outlet. You could even use a battery powered device there.
That creates a virtual control for the outlet. The switch send a radio message to the hub (or possibly directly to the outlet, depends on the specific models you choose) And then the outlet turns itself on or off.
For example, this outlet
Plus this battery powered wall switch
Would be a good combination. (Just put a blank plate where the existing wall switch is, or a little box cover over it, and then put the battery powered switch there.)
You wouldn’t have to do any wiring for the wall switch and replacing the outlet should be pretty straightforward, but again, follow the wiring diagrams that come with the smart switch, don’t just try to duplicate the existing wiring.
Oh, and take good pictures of the existing wiring before you remove it, including at the screw connections. You can thank me later.