You can’t use the GE auxiliary switch, because it doesn’t have a radio in it and it’s actually invisible to SmartThings. It communicates with the matching GE master switch with physical traveler wires.
The most popular options of the mains powered switches are the Linear/gocontrol auxiliary switch or the Cooper that you mentioned previously.
https://www.amazon.com/Linear-Z-Wave-3-Way-Accessory-Switch/dp/B00EAY3K5Y
If you want to go with one of the battery powered options, see the following thread: