According to a skim of the
NHL Trade Tracker website, I'll nominate ... On November 28, 1918, the Montreal Canadiens traded centreman Tommy Smith to the Ottawa Senators for cash. The "winner" in that transaction was clearly Montreal, considering the Canadian economy nearing the end of The Great War.
As for the first player-for-player trade, I'll suggest ... December 14, 1919, the Quebec Bulldogs traded forward/defenceman Goldie Prodgers to the Canadiens for defenceman Ed Carpenter. Best I can tell, George "Goldie" Prodgers (or "Prodger" according to other on-line sources) wasn't actually on the Montreal roster until 1925-26, and his record shows all zeroes for that year. At least Carpenter contributed 11 points in 24 games for Quebec in 2019-20. So I reckon the Bulldogs "won" in that trade.
IMPORTANT NOTE: Player records this early in the life of the NHL should be considered anecdotal, based on a few cross-references I made between NHL Trade Tracker & the
Hockey Reference website. Even the player profiles linked in Trade Tracker (pulled from the
hockeyDB database) show inconsistencies within their trade listings.