Hawaiian Airlines is debating whether to launch basic economy class, a bare-bones product that other carriers love because passengers will pay more to avoid it.

The airline's challenge is how to offer a bare-bones class of service that doesn't insult passengers in the process, Hawaiian Airlines' CEO Mark Dunkerley told CNBC.

Hawaiian Airlines is tiny compared with other U.S. behemoth airlines, but its home market is growing rapidly amid a boom in tourism to the islands.

Cutting certain perks that are currently free could backfire, said Dunkerley, who is retiring early next year.