Here's a list of the players who've had the least ice time per game of the last 11 seasons, with a minimum of 164 games played:

It should be obvious that there's really only one talent that will keep you in the NHL for a lengthy career without you being able to play a regular shift.  Amazingly, there really isn't anyone who got fewer shifts per game than Peters but managed to play even 40 games in their career.  The last column is how many penalty minutes each player got per 82 games (x60 minutes) of playing time.  Peters is head and shoulders above the rest of the league's regular goons in terms of his sheer efficiency in getting penalties.  The only real contenders are found among fighters with shorter careers:

We really only have two contenders: Peters, and David Koci.  Koci gets quite a bit more ice time than Peters, but he also gets even more penalties.  But clearly it would be difficult to challenge Morissette, who had either a major penalty or a misconduct in 7 of his 11 career NHL games.