Are there successful, non-surgical techniques for gallstone removal?

Not really. Gallstones in the gallbladder under the liver cause nausea and pain. They can block the ducts or tubes that drain the liver or pancreas causing jaundice or pancreatitis if they pass from the gallbladder to these tubes. Some drugs have been used to dissolve small stones; but the treatment is long, and the stones return when the drug is stopped. Ercp can be used to remove stones in the bile ducts.
Yes, but... ....I recommend surgery. Back in the 1980s, when we first developed lithotripsy (shock wave rx) for removal of kidney stones, we experimented with this for gallstones. Similarly, there are medications that can dissolve some gallstones. Alternative therapies advocate "gallbladder flushes". Unfortunately, all of these leave behind the "gallstone factory"; the best treatment at present is surgery.