As long as the grease is a multi-purpose waterproof grease it'll be fine.
With regard to getting the old prop off as long as the engine has been regulary serviced the shaft should be well greased anyway and just fall off
. However sometimes they stick
The best option is to use a block of wood and gently tap the back of the blades. Make sure you tap each blade and not just one as this may damage it. Once out far enough you can then get a screw driver behind itand lever it off.
One other thing is make sure the thrust washer does not stick to the back of the old prop. Its quite important!!