The calcified rock sat in vinegar for two weeks, then Mr Dwyer scrubbed it down with a toothbrush for 12 hours, he said.
"Then I saw the numbers. That's what got me, when I saw the start date and the end date I knew what it was."
Engraved on the urn's slim neck, in flowing script, is 01.09.63 - 26.09.86. The name above the dates reads Shane Micheal Williams .
Mr Dwyer said he was saddened to learn what it was he'd found.
"The guy was 23-years-old. That's three years younger than me. He died in the same month he was born, that's really sad.
"I wish it had a big tag on it saying 'urn'. I would have left it in its place," he said.
The urn is adorned in different patterns including weave-like images and gridded circles.
Also engraved were the words: 'In our lives you left your soul, in our hearts you left your mark'.
Mr Dwyer's priority now was to return the urn to Mr William's family.
"I've been trying to track his family down.
"I've been googling them and going through the library records trying to get anything I can find on them."
But Mr Dwyer has had no luck. He hoped to try to reach them by sharing his story with the Bay of Plenty Times.
"For someone to take it out into our harbour, they must be local," he said. "I'm sure they will want him back."
The urn had been found near the Maori warrior statue, on the Port of Tauranga side of Mauao.