Now to practicalities:
As stated, your 120V straighteners will work (as long as they don't exceed the maximum permitted power rating). Several people have posted on AB to state that their UK (240V) hair straighteners work on 110-120V systems, but that they take ages to heat up. (If you're taking your mobile phone, people have also reported that they've managed to get a very small charge on their phones on a 110-120V supply).
Most of the power that goes into a hairdryer goes into the heating element. The fan uses relatively little power. So simply switching to a lower speed won't drop the power consumption down very much. (e.g. it might go down from 650W to 600W but it certainly won't get close to the 300W limit).
You need to check on board the ship to find out exactly what the rules are. If the circuit in your cabin is set to trip out at a very low current, you won't be able to use your hairdryer. However, it might just be that the circuit supplying a block of cabins has a maximum power rating. It might be possible to use your hairdryer as long as you don't do so when all the other occupants are also using theirs. That could be why you need to check with reception first.
The MS Royal Star is over 50 years old. It's electrical circuits weren't designed for the multitude of todays appliances. However, I'm sure you'll have a great time:
http://www.manchesteronline.co.uk/travel/revie ws/s/156/156610_cruise_ms_royal_stars_indian_o cean_odyssey.html
Chris