Both players are now free agents.
In 50 games with the Blue Jays, Shaw hit .239/.306/.411 with six home runs. He was projected to earn between $4.2 million and $5.4 million through arbitration this winter, according to MLB Trade Rumors.
Cole, 28, was effective out of Toronto's bullpen in 2020, posting a 3.09 ERA and 1.20 WHIP with 20 strikeouts over 23 1/3 innings of work. He was expected to earn between $800,000 and $1.1 million in arbitration.