Why are you planning on removing the caulking? Is it dried out, separated, etc? Or just to make it look neater?
If neat is what you're after, and the caulking isn't separated from the wood. Then DON'T start cutting the caulking out. I did the whole deck on Island Breeze, a 56 footer, and let me tell you, it is a lot of hard work.
If all you're trying to do is get the teak smooth again, just sand it and the existing caulking. For cockpit seating, I'd use 80-100 grit and then hit it a second time with 220 grit using a DA sander. Just remember to tape around the wood so the sander doesn't hit your gelcoat, paint, or whatever.
In the event you do need to remove the caulking, it's a tough job. Tedious, boring, and labor intensive. You have to get all of the old caulk off the wood, not just most, but all of it. I used a Dremel tool with a router adapter and a straight 1/8" carbide burr that I intentionally dulled on a piece of stainless. That made it dull enough so it would still cut the rubber on the edges of the wood, but it wasn't sharp enough to really damage the teak. It takes a light touch and a lot of patience. (And I'm just a little short on the latter.)
Next thing, after the seams are completely clean of old caulking, you need to lay a layer of 'Klean-Edge' tape in each seam. This is so the caulking doesn't stick to the fiberglass deck itself. You want the new caulking to stick to the sides of the seam, but not the bottom. (It'll heat/cool/stretch/pull and tear itself loose from the wood if it's attached to the fiberglass).
I've heard pros and cons as to whether you should strip the caulking out, sand the teak first, then apply new caulking, or strip the old stuff, put in the new stuff and just sand the whole thing at one time.
I used the latter method. I stripped the caulking out, used the Dremel to get the last of it off the wood, vacuumed everything two or three times, wiped everything down with acetone (necessary step to help leech out some of the oil in the teak--it helps the new caulk to bond.) Then I put the tape in the seams--a hassle, for sure, and applied the new caulking. BTW, I used Teak Deck Systems caulk. It's a little pricey, but it works. The original stuff got gooey when it got hot. It was made by Sika company, and I don't think it was meant to be used in the tropics. The Teak Deck Systems stuff didn't seem to care how hot it got outside. It was easy to use, sanded well and left a beautiful finish.
Good luck, and I hope this helped.