The only way to replace the line is by running a new line through the tube; you can do that easily by using the existing line to pull the new line through. Either end works: from the cockpit or from below. The pendent line attaches to the centerboard with a shackle. A clevis pin goes through a hole in the trailing edge of the centerboard, which is attached to a shackle, which is held by an eye loop in the pendent line. The pendent line goes into the centerboard slot, through the tube you mentioned, and runs up to the cockpit.
Simple to replace. From the cockpit: remove the grommet at the bridge deck that surrounds the line. Attach the eye of the new pendent line (the part that will attach to the centerboard shackle) to the end of the pendent line in the cockpit. I used duct tape, but you can sew them together for an even smaller profile. Put the grommet on the end of the new line, and tie a stopper knot at the end of the line. You are about to pull the new line through the tube using the old line, and the last thing you want is to pull it too far!
Go below the boat to the centerboard. Remove the existing shackle from the centerboard. This is done by removing the cotter pin from the clevis pin. Pull the line down, pulling the new line through the tube. Once the end of the old line pulls through the eye of the new line, remove the tape that holds the two lines together. Put the shackle through the eye of the new line, and attach it to the centerboard. As long as you are replacing the line, I recommend replacing the shackle, clevis pin and cotter pin too. Back in the cockpit, reattach the grommet to the bridge deck and adjust your stopper knot to allow the board to go down as far as you like.
What to use for a replacement line? Rudy at D&R Marine sells a direct replacement for the Oday 23/25 pendent line.
http://www.drmarine.com/proddetail.asp?prod=DR80-01
You need a narrow width shackle that might not be easy to find (it has to fit in the centerboard slot without sticking), and Rudy has them and the proper length line already made up. I actually did some research when replacing my line, and I think you might be able to purchase the line and shackle a bit less expensively if you are willing to put in the effort, but you can't beat the convenience of ordering right from Rudy. Saving two dollars didn't seem worth it to me. I went with my man Rudy. And if you have one of those old fashioned rope-to-wire pendent lines, don't worry about replacing it with an all synthetic line. There is no longer any reason to put up with those dual material items: no-stretch line is now cheap enough for all, so we don't have to worry about that rope-to-wire mechanical connection
Can you do the line replacement with the boat in the water? I sure couldn't. Not even close. When the clevis pin on my line failed (or fell out because the cotter pin failed), I dove under my boat just to find out why my line wasn't working. I barely had enough time underwater to figure out what the problem was, let alone fix it. I wound up sailing the rest of the summer with the board all the way down, and replaced the line when I hauled the boat out of the water at the end of the season.
Good luck.