Hamilton, 33, played 12 seasons in the AHL from 2006 to 2018, skating in 644 regular-season games with Houston, Toronto, Oklahoma City and Bakersfield and serving as captain of the Condors for the last three years.
Hamilton totaled 197 goals and 179 assists for 376 points and was an AHL All-Star in 2012 and 2013.
The native of Oshawa, Ont., also played 40 postseason games, collecting 10 goals and six assists for 16 points. He reached the Calder Cup Finals with Toronto in 2012.
Hamilton played 30 NHL contests in his career, earning one goal and four assists for Toronto and Edmonton.
Cote, 36, spent 10 seasons in the AHL between 2003-04 and 2014-15, appearing in 623 regular-season games as a defenseman with Hamilton, Wilkes-Barre/Scranton, Norfolk and Syracuse. He notched 22 goals and 100 assists for 122 points.
Cote won Calder Cup championships with Hamilton (2007) and Norfolk (2012), and reached the Finals with Syracuse in 2013. He registered two goals and 13 assists in 61 career playoff games in the AHL.
A native of Quebec City, Cote tallied four assists in 27 career NHL games with Montreal and Tampa Bay.