If I remove the drive shaft, will it free up the vehicle so I can move it to work on it without doing damage to the transmission?

You don't even have to remove the driveshaft. They get pushed around all the time with the engines not running. All you have to do is shift it out of "park". All the other gears will be in "neutral" when the engine isn't driving the transmission. In fact, every gear will be as though it's in "neutral" except that when in "park", there's a spring-loaded mechanical finger that swings into position to hold the driveshaft from turning.