From picture, there is not enough room to get in there and get the old packing out. I would dry dock, drop the rudders, unscrew gland (you can use a pipe or chain wrench on the round part of packing gland), and clean out and repack the glands on a workbench. Then reinstall gland with a couple of turns and put rudder shafts back up,and snug up back in the water. I have slightly more room on my 1976 43 DC and that is how I did mine. It would be impossible to unpack old flax otherwise. I have done the prop shafts in the water several times, enough room and packing 'new enough' not to shred when you get a hold of it. Water intrusion not that bad, but I wouldn't do it with your rudder glands as packing is probably 30 years old and hard as rock. As for what type, I used the Gore type in my rudders, but that stuff is unforgiving if you over-tighten (it will leak and you will have to do the entire job over again). For something like rudder that doesn't turn much, I think the old cotton/wax type flax is fine and perhaps even preferable. Note that when I dropped my rudders (I was in gravel boat yard and dug small holes underneath each to drop all the way out), I found the rudder shafts needed a good cleaning (don't overdo it!, easy to reduce diameter of soft material with sand paper) and that the port rudder shaft top bushing (above the stuffing box) has slop in it that I replaced (Sams stocks them, but I had to drill mounting bolt holes). I also stripped rudders of old paint while on saw horses and gave them the mastic epoxy coating (Interlux 2000) which allowed the antifouling paint to not flake off for about about 6 years.
ps: Beware the rudders are really heavy, you will need a car jack to get them back up.