Looks like you have a traditional stuffing box. Without removing the prop there is no way for the shaft to pull through into the boat
. The shaft won't push it's way out of the boat
when it is stationary. If you sail or tow the boat it is possible to loose the shaft. The packing might leak a bit if you pull the shaft into the boat and the shaft is dirty with marine
A Dremel tool is not up to the job of cutting off the coupling - an angle grinder with a cutoff disk is the tool to use. Cut until you are close to the shaft but don't cut into the shaft. Do the same on the other side. Drive a wedge into the cut to crack the remaining part of the shaft.
I had to do this once on my present boat. After that I started spraying the coupling with Boeshield T9 periodically and the coupling looks like new.