Do solder-mount screws exist?
Surface mount, reflow solderable stand-offs are available, for low mechanical stress applications. 

See for instance the PEM ReelFast SMT product range. They offer spacers, nuts and snap fasteners in a range of sizes. These do not require plated through holes.

The parts come in the reel with removable Kapton patches on top, covering the holes, for vacuum pick-up, so they can be used for pick-and-place assembly as well.