As previously stated, you seem to have a non-standard brand stuffing box.
If it were me, I would prefer to do the packing replacement while above water as you may not know how much flow you will get into your boat - many people do replace their packing in the water.
The other suggestions posted about stemming the flow make a lot of sense as well if you choose to do this job while your boat is still in the water. Toilet bowl wax and plastic wrap around the shaft exit point can help reduce the water ingress as far as I have heard.
You have no way of knowing what size packing material you will need until you remove those 2 bolts and move the plate forward and measure it with a caliper (or at least a finger tip). I highly recommend using Gore GFO packing and nothing else: Virtually Dripless Packing by Gore GFO
Instead of waiting to measure the aperture of the stuffing box you could purchase
several sizes of this packing material, say: 3/8, 5/16, 1/4" sizes should cover you but I just hate surprises so I bought the same array of material before I did mine on the hard
Here is a tutorial for a "normal" stuffing box repair that is one of the best on the web: Re-Packing A Traditional Stuffing Box Photo Gallery by Maine Sailing at pbase.com
This job is normally not so difficult once you get into it.
Good luck and keep us posted.