There aren’t too many hockey players with the skill to be an offensive weapon and the spunk to be an agitator. The Lemieux family has two.

But there was a time when Claude Lemieux — the four-time Stanley Cup champion and notorious troublemaker — wanted to steer his son Brendan, the tenacious 23-year-old winger for the Rangers, away from pursuing the sport.

“I just thought it would be really hard for the son of a dad that played to follow in your father’s footsteps,” Claude, now 54, told The Post in a recent phone interview. “Number one, I think it could be brutally unfair at times, and it was and it has been at times throughout his young career. And especially the way I played, I wasn’t a player that was very popular aside from the team I played for and the fans that I played in front of, the home fans, so I thought that would be a difficult path.

“But at the end of the day, it’s what he wanted to do. I realized when he was around 9 or 10 years old that he was one of the better kids and that he seemed to have what it would take to become a hockey player.”

Brendan was alive for the last two of Claude’s Stanley Cup triumphs. There are pictures of baby Brendan inside the cup after the Avalanche won it all in 1996. And Claude recalls how Brendan badly wanted to sleep with the famous trophy — Brendan has no such memory — after he won it in a second go-round with the Devils in 2000.

Claude — one of 11 players in history to win the Cup with three different teams (he also won with the Canadiens in 1986 and the Devils in 1995) — fondly remembers Brendan slipping into the roller blades of his two older brothers, Chris and Michael, when Brendan was just 18 months old. By the time his second birthday rolled around, Brendan wanted a skating party. But Claude did everything he could to push Brendan toward baseball and golf, away from hockey. His mom, Deborah, was the “catalyst.”

“She gave me that initial push and then my dad pretty much took over once he saw a few games,” Brendan Lemieux told The Post.

There were sacrifices along the way — cancelling the family’s Christmas-time ski trips in order to travel to Brendan’s tournaments, for instance — and it hasn’t always been easy for the elder Lemieux to navigate the relationship with his son. Claude recalled a time at the beginning of Brendan’s professional career when he was critiquing his son’s game. Brendan told him, “You have to let me live my life, you have to let me play my career, you can’t do it for me. I’ve got to learn from my mistakes.”

“There was only a couple of years where it was kind of a challenge,” Brendan said of the pressures of following in his father’s footsteps. “But once you’re past that, it’s gravy from there.”

Lemeiux, repeatedly referred to as a mirror image of his father in scouting reports as he developed (both are listed at 6-foot-1, 210 to 215 pounds; Claude was a righty shot, Brendan shoots lefty), was drafted by the Sabres with the No. 31-overall pick in 2014, subsequently dealt to the Jets and acquired by the Rangers at the trade deadline last season along with a first-round pick in exchange for Kevin Hayes.

Brendan said he modeled his game after the way his father played from watching old tapes and getting to see his Claude play during his brief comeback with San Jose in 2009 at the age of 43. And he knew if he played the same way, it would hurt, recalling the bumps and bruises his father came home with on a daily basis.

“I look at all the sons of fathers that played, and I would say that 9 out of 10, if not 9.5 out of 10, those boys are all dedicated, hard-working and they play with passion and they know from their dad how fortunate they are to be playing this game,” Claude said. “They don’t take it for granted.”

Now, the roles are reversed as Claude studies Brendan’s game, watching his son compete for a team he tormented in a series of memorable postseason encounters. Claude, who is also Brendan’s agent, can’t help but ask, when he sees other players chirping his son on the ice: What are they saying about me?

“That’s always funny,” Brendan said. “I kind of like it when they say it, because it really sets me up to let them know … the guys who are willing to say that are definitely not half as good a player as he was.”

Claude said he thinks Brendan is getting closer to the player that he can be. Brendan has compiled nine points through 22 games and has three goals, including a game-tying short-handed score in the Rangers’ come-from-behind victory in Montreal on Saturday. But Brendan won’t light up the stat sheet every night, and it’s the intangibles that have made him so valuable to the Rangers. Witness the three fights, broken blade and missing teeth in the last month alone. Those are intangibles that come from an elite bloodline.

“I’ve always been pretty outspoken about [how] the closest player comparable to myself is my dad,” Brendan said.