As a free agent from the Lightning after the completion of his entry-level contract, Kunyk signed a one-year deal with German-based club, Grizzlys Wolfsburg of the DEL on August 18, 2015.[3] After training and competing in four pre-season games with Wolfsburg, Kunyk was released from his contract unable to reach the expectations of play on September 6, 2015.[4] Kunyk later signed with Danish club, Gentofte Stars of the Metal Ligaen for the 2015–16 season. Kunyk made an immediate impact with the Stars and in 27 games, placed second in team scoring with 13 goals and 29 points.
In the following off-season, Kunyk returned to North America as a free agent, securing a one-year AHL contract with the Utica Comets, an affiliate to the Vancouver Canucks on July 25, 2016.[5] Kunyk responded to his return to the AHL with a career year offensively in posting 15 goals and 37 points in 61 games.
As a free agent, Kunyk opted to return overseas in signing a one-year deal with top flight Finnish club, SaiPa of the Liiga on September 5, 2017.[6]