Based on this risk, shipping companies prohibit the use of straighteners, even the vast majority of them also prohibit hair straighteners on boardSince this is a question that generates a lot of controversy, I am going to leave you the link of the main shipping companies where you can see the list of prohibited objects
Costa
Power tools, kitchen appliances and items that have heating elements (e.g. immersion heaters, electric blankets, infrared heaters, hair straighteners, water heaters, coffee machines, etc.). Complete list
MSC Cruceros
Port security personnel are required to search passengers and their luggage in order to confiscate those objects considered dangerous at an international level that may put the safety of passengers, crew and the ship at risk. Such items will be confiscated and will not be returned: alcohol, firearms, sharp objects such as blades or scissors, flammable and explosive material, objects with heating elements or open flames (such as clothes irons, kettles, stoves, hair straighteners, candles, incense), drones, Samsung Galaxy Note 7. Firearms, explosive material or illegal drugs will not be allowed on board; in case of detecting them, the authorities will be notified immediately. MSC Cruises will be obliged to deny access to any passenger who does not comply with these mandatory rules. In the interest of health and safety, neither food nor beverages (including partially consumed or home-cooked food) may be brought on board. Dry, packaged and commercially produced foods will be excepted from this rule. Complete list
Royal Caribbean
Candles, incense, coffee pots, irons, travel vaporizers and electric stoves.& Objects that generate heat or produce open flames. These include heating pads, irons, electric stoves, candles, incense or any other object that could cause a fire. NOTE: The only exception to this policy is curling tongs and hair straighteners. Normal matches and lighters are allowed on board. However, “”torch-type lighters”” and gun-shaped lighters are not allowed on board. Torch lighters emit a powerful concentrated flame and are therefore prohibited. Comple list