As far as I recall all of the Oasis balconies have glass all the way to the ground, so there is no way he could fall over unless he is a climber and you leave a chair and table just right.
That would certainly be a tragedy - but it seems to be one of those somewhat irrational mom fears.
Yes, you can walk to a very quiet and pleasant beach in St. Martin, about 15 minute walk.
In Nassau going to Atlantis for the day is the best bet.