Use a line with a very hard, abrasion resistant cover. 5 mm Marlow Prestretch or New England Ropes Finish Line are good choices.
This is best done while the boat is on a trailer, high enough to drop the board completely.
Remove the handle and lower the board slowly, catching it with your other hand. The spring will fall out, so be ready for it. Unhook the board from the pivot.
Cut the old line off, and now's a good time to fill dings and scratches on the board.
Feed the new line through the hole in the top of the board and tie an overhand knot. Make sure it's seated completely. If this knot comes undone, you'll lose a spring ($$) and maybe the whole board ($$$).
Put another overhand knot in the line, about 1" above where it exits the board.
Lower a piece of scrap line through the deck fitting and tape it on to the end of the new line. Hook the board on the pivot and replace the spring, holding it in place with a finger as you raise the board with your other hand (take up the slack in the line so it doesn't get pinched). When the new line appears through the deck, grab it and raise the board all the way, setting the knot in the deck fitting.
Tweak the location of the knot so that the board is nearly flush with the bottom of the boat when it's cleated in the up position. This might involve lowering the board out of the CB trunk one or two times so you can move the knot.
Retie the handle 12 1/2" from the bottom of the hold-up knot to the part of the handle that won't fit through the deck hole. DO NOT MAKE IT ANY LONGER - there are side supports in the hull meant to line up with the "hump" on the top of the board and if the line is too long, the board will go sideways through the trunk. Don't ask me how I know.
If you can see the notch on the trailing edge of the board when it's fully down, the line is too long.
This goes a lot faster if you have an extra set of hands, but it's a fairly easy job for one person.