I suspect adding a small amount of water has a similar effect to letting the water cool to 95C - I certainly assume the heat capacity of "a little bit" of water

I suspect adding a small amount of water has a similar effect to letting the water cool to 95C - I certainly assume the heat capacity of "a little bit" of water is less than a full press. So, sure, skip the water&stir - but be mindful of the temperature.