The numbers you gave are not compatible. The 14v battery has less power than the 11v. Laptops need AmpHours. Most are not sensitive about total voltage, because the charging-circuits take care of it.
The 14v will probably fit... but it will not last as long. That means: No movies on the airplane !
Does the charger get HOT ? with the laptop OFF ? with the laptop ON ?
What is the specs of the charger ?
Its your call, my wife's big-screen ASUS stays on her desk. Its battery-less :>)