They see their quasi-celebrity status as a chance to build up the sport in the Cayman Islands, where N.H.L. games are regularly shown in sports bars and roller-hockey and ball-hockey programs have been in place since the 1980s.
“We’re trying to promote the game,” Klein said. “This is not just a bunch of old guys living their dream.”
Christine Maltman, Klein’s wife, successfully pitched a fund-raising idea, incorporating a weekend hockey camp, to the Lightning. Three dozen youngsters from the Cayman Islands took the ice in 2011 with the former N.H.L. players Dave Andreychuk and Brian Bradley. They were also treated to a postgame meet-and-greet with the Lightning’s captain at the time, Vinny Lecavalier.
While hockey has been making inroads in warmer climes — Auston Matthews, picked first over all in the 2016 draft by the Toronto Maple Leafs, grew up in Arizona — no one is expecting a star to come directly out of the Cayman Islands anytime soon.
But that does not mean that potential N.H.L. talent cannot start out in the islands.
One current team member, Darren Lawrence, a partner at an accounting firm chartered in New Brunswick and a former Junior B player who spent time on a line with Joe Thornton of the San Jose Sharks, moved his family back to Canada so that his son Josh, then 6, could trade roller hockey for the real thing after showing professional potential.
“We wanted to move back before he would start to miss out on the key development ages for hockey,” Lawrence said.
Josh, 15, is now attracting the attention of coaches and scouts while playing at a hockey academy at South Kent School in Connecticut. He is considering how best to further his career and is projected to be a future N.H.L. draft pick.
“He is trying to decide if the Quebec Major Junior League or the N.C.A.A. is the right way to go for him,” Lawrence said.
Though Lawrence still plays with the Breakaway despite his return to Canada, the rest of the team has stayed put with members having spent more than 20 years in the Cayman Islands.
“This is home,” said Klein, who has a teenage daughter and son.
But for one week a year, home is a sheet of Canadian ice under their feet. With a splash of rum.