Exhibit A: 1954 - same team, but a year before Skinner took over.
from 7 mins 13 seconds, you can see them kissing it and hear the commentator talking about the victory kiss.
Exhibit B: Possibly 1950
This photo of Lindsay kissing the Stanley Cup has been dated as 1950 by the seller ("the first of four Stanley Cups" for Ted Lindsay.
Here is a true classic of Hockey in Detroit in the 1950's. It is a photo of Detroit Red Wing captain Ted Lindsay kissing his first of 4 Stanley Cups. The Wings won the cup in 1950, 1952, 1954, 1955. This is a 16x20 inch photo of Ted Autographed and framed. He added HOF 66 refering to his induction into the Hockey Hall of Fame. This framed item also is complete with a plaque as to Lindsay's great career."
Exhibit C: Earlier than 1950
It is widely acknowledged that Lindsay began the tradition of bringing the cup around the rink in a victory lap.
One example, from https://en.wikipedia.org/wiki/Ted_Lindsay
"Lindsay was the first player to lift the Cup and skate around the rink with it, starting a great tradition. During a 2013 signing in the Greater Vancouver area, Lindsay is quoted as telling a fan that he didn't mean to start a tradition, that he only wanted to bring the cup to the rinks edge where the fans could see it. He did not lift the cup above his head at that moment, as was adopted in subsequent years."
I propose that if the kissing tradition was also started by Lindsay, this would be mentioned along with the acknowledgement that he started the victory lap.