No, that's not the right applicator for the HSS tags. The tags are metal and need one part to be bent over the other once they're through the ear.
As Big Light says, apply directly to Ketchums. They used to give the applicators away with your first order. It's worth a try, but they'd stopped by the time we got ours.
An alternative would be for an ex-HSS member to pass on their unwanted applicator.
Love the title of your thread