Many times an All-Star player during his junior career with the Prince Albert Raiders, Viveiros, a skilled defenceman with soft hands, was drafted to the National Hockey League by the Edmonton Oilers in the 6th round of the 1984 NHL Entry Draft, 106th overall. He however never played for the Oilers, having been traded to the Minnesota North Stars in a five players swap, along with Marc Habscheid and Don Barber for Gord Sherven and Don Biggs. With the North Stars he did get some NHL playing time, although only very limited - a total of 29 games spread over three seasons, with a total of one goal and nine assists, playing most of the time in the International Hockey League with the Kalamazoo Wings. He never played in the NHL again; he did sign with the Hartford Whalers as a free agent on February 9, 1990, but that signing did not materialize into anything but minor league playing.
In 1991, Viveiros packed his things and moved to Europe. He joined EC Villacher SV, thus begining a long journey in Austria and Germany and Italy, that even led to him gaining the Austrian nationality along the way, in 1998. Viverios was among a handful of players that was lobbying the International Ice Hockey Federation for permission to play for a country other than his own in the Salt Lake City Olympic Games in 2002, despite having played as a teenager for the Canadian National Team at the 1986 World Junior Championship. He failed both times, as the International Ice Hockey Federation forbids players who have already played for one nation to line up for another one at a later time, to minimize some countries' tendencies to build their national teams around mercenaries rather than around local players and help foster the development of those nation's homegrown players by giving them the chance to play in international competitions in lieu and place of the mercenaries. His request was therefore not granted. However, he was allowed to represent Austria at the 2005 World Championship, two years after the International Ice Hockey Federation decided to review its rules on the matter and set a new rule, stating that a foreign player may represent another national team if he has played four straight seasons in the domestic leagues of his adoptive country. Unfortunately for him, his stay at the World Championship was short, as he was injured on May 8, 2005 in a game against Denmark. He was also eligible in 2004, but was sidelined with a groin injury ad couldn't be selected.
In 2008, Viveiros returned to hockey as a head coach, with EC KAC.