I use a
single edge razor blade, and put a little bend in it with my thumbs, so that the outer edges don't catch on the teak. I pull it toward me, do what I can reach, and then move forward or backward a couple of feet. It works well, and the blades are
cheap. Buy a pack of 100 at the
hardware store and throw them away as they get dull. Much faster than a chisel. You'll have to stop and sharpen the chisel more often than you think, and it's easier to gouge the teak with a chisel.
Do a few minutes every day until you finish, or get some knee pads if you're determined to do it all at once. Repeat every few years.
To clean out the old caulking, I once ground a Red Devil scraper to the proper width. I used it until I discovered the Fein tool with the
teak deck blades. It works so well that you'll want to recaulk your
deck often, just so you can use the tool.
Applying new caulking is messy until you get the hang of it, but if you mask the
deck seams and plan carefully, you can learn to do it neatly without much trouble. I recaulked our decks with polysulfide 20 years ago to recover from the "care" lavished on them by a former owner, who had oiled them regularly. Since then, a day or so of
maintenance every two or three years is all that's required. Our
boat is sailed constantly in the
Caribbean, so it gets frequent saltwater washes. That helps, I think.