If it's only for tethering a goat , then why not use a horse tie up ring , We have collars on all our goats and the milking stand has a simple clip on arrangement like a lead rope , after all ,you're not anchoring the QE2. Keep it short to restrict head movement to the feed bucket only , she will soon get the idea. One of our togs was a maiden milker and would leap about and kick the teet cups off for the first three days, then she got used to the routine and now lifts her leg for you to pass the pipework under.
A cow chain will be too big for a goat, but a dog collar gives you control.