According to a death notice for Mr Schaaf, he was 35 years old, died on November 1 and lived in the Queensland town of Mareeba.
He is survived by his partner Billie Jo Johnson and six children.
And like his famous cousin, Mr Schaaf was also a keen rugby league player, involved with the local Brothers Cairns Rugby League Football Club.
Messages of support had been posted on the club's Facebook page after news of Mr Schaaf's death spread.
"The club is terribly saddened by the sudden passing of Tony 'Sass man' Schaaf," a post on the page stated.
"A quality player, fantastic club man, and a friend to all, he will be deeply missed. Our thoughts and prayers to all of Tony's family and friends at this time #foreverourbrother."
Mr Schaaf was buried at Mareeba Dimbulah Rd Cemetery on Saturday.
Meanwhile, Williams is yet to make a decision about whether he will leave the All Blacks Northern Tour - due to finish on November 23 after tests against Scotland and Wales, for the birth of his first child.
His manager, Khoder Nasser, told the Herald on Sunday before yesterday's match that it appeared Williams would stay on until the end of the tour, but that could change.
Twickenham's '100 TV replays' start to annoy Hansen
It wasn't all smooth sailing for the All Blacks yesterday morning. They battled through a slow start and survived a controversial second-half sinbinning to beat England 24-21 at Twickenham.
Watch: Hansen 'TV producers annoy me'
Skipper Richie McCaw had a star role in the victory, adding another try in the black jersey to his collection.
Aaron Cruden and Charlie Faumuina also scored tries.
Hooker Dane Coleswas sinbinned in the 57th minute.
After the match, coach Steve Hansen questioned the influence TV producers have in rugby games. "TV producers, they're starting to annoy me," he said. "If something goes wrong we might see a replay 10 times. The referee hasn't seen it, the touch judge hasn't seen it, the TMO hasn't seen it. We need to bring in a challenge so if a player or a coach has seen it he can challenge it, but if they don't see it we don't need a TV producer to replay something 100 times."