Falk is coming off a Calder Cup championship season with the Lake Erie Monsters, with whom he tallied two goals and seven assists in 32 regular-season games and four assists in 17 postseason contests in 2015-16.
The 27-year-old Falk also appeared in 24 NHL games with Columbus, tallying four assists.
A native of Snowflake, Man., Falk has recorded two goals and 21 assists in 171 NHL games with Columbus, the N.Y. Rangers and Minnesota. He also has nine goals and 33 assists for 42 points in 260 career AHL contests.
Falk was a fourth-round draft choice by Minnesota in 2007.
Fedun, 28, posted eight goals and 25 assists for 33 points in 63 AHL games with the Utica Comets in 2015-16. He also had one assist in one NHL game with Vancouver.
Over four professional seasons, Fedun has skated in 263 AHL games with Utica, Worcester and Oklahoma City, recording 32 goals and 100 assists for 132 points with a plus-23 rating. He has added two goals and five assists in 12 NHL contests with Vancouver, San Jose and Edmonton.