I'd say definitely lock the shaft - you'll have enough difficulty using the puller underwater as it is.
I'd suggest you tie something on the old prop - they can "pop" off the shaft with some force and it might go for a swim if it turns out to be on real tight. Maybe leave one nut loosely on the shaft as a preventer....It's a good spare. When you use the puller stay to one side - don't be in the line of fire.
You might give the end of the shaft a good smack once the nuts are loose - this may pre-loosen the taper fitting, but use a soft hammer or a brass drift so as not to damage the threads.
The new prop should go on easily if everything is clean. Some never-sieze shouldn't hurt.
Since its a 326 it hasn't been on there for 20 years, so things should go OK - but it's a much easier job to do on the hard.