What are the risks of sending low-current neutral through the ground wire?
Yes there are risks to safety.

If anything interupts the ground conductor that leads back to the service entrance, suddenly your switch is energizing the ground on that circuit, so anything connected to it is also going to be energized (i.e. a printer that has a grounded metal chassis suddenly has a live metal chassis).

You guess that this is only a few milliamps, but do you know under all operating conditions that this is the case? Just 10mA is enough current to cause muscular paralysis -- and 100mA is fatal.

You may think that "well yeah, but it would take multiple bad things to happen for this to be a safety hazard"... but you're already doing one of the bad things it would take, so you're one conductor away from a very unsafe situation.

There are some smart switches rated for use without a neutral (but they generally only work with incandescent lamps).

Since you're just controlling a receptacle, the easiest thing to do is use a plug-in lamp or appliance module. 

But if you were controlling a ceiling light fixture, you could use an in-line switch module that wires in at the lamp fixture itself instead of at the switch:



You could keep the switch on all the time to supply "line" to the lamp fixture, and use the existing neutral at that fixture, then let the switch module control power to the lamp. Then you can use a batttery operated wall switch to control the lamp module.