Yep. Get an 11.8v NiMh that is big enough to do the job. If you'll check the amp draw on your hovercraft and multiply that by the amount of run time you need in hours, that will tell you how many amp hours you need. Multiply that number times 1000 to get Mah, which is how RC batteries are generally measured.
Of course, you'll draw more amps with the battery attached since the hovercraft will weigh more. That will require more battery, which will then require more amps. So the fan you tested may or may not work. Designing things is hard. I teach engineering.