With pain in my heart I decided to get rid of the teak deck on the left and right of the cabin, plus the teak that was on the front deck of the boat. After some breaking and hammering I found out it was definitely the right thing to do. Under the teak boards was still a lot of moisture and there was no way of really making that part of the deck waterproof because I could not excess the sides (and there where huge holes where water could get under the deck). Also I was not entirely sure that by re-caulking this part of the deck, the new walls of the cabin would be safe from water damage which could risk them getting rotten once again (which would mean a lot of work done for nothing).
It was way to easy to remove the teak boards. Just unscrew the screws and one could easily pick them up from the deck (the glue that was used to hold them was corroded away). So all, in all a good decision. One problem though, the stuff underneath the boards. My god, that was some heavy-duty (almost cement like) substance!
So I got a powerful belt sander with high-grade, large grain sandpaper to battle that nasty stuff. Still it took almost two hours to sand one cubic meter of deck, but it got the job done beautifully.
After that, some other parts that where connected to the deck (like the hatch) needed to be repaired, to be absolutely sure that water could not get to those as well.
The screw holes that where in the deck to hold the teak boards also needed to be made a little bigger, so those could be easily filled with epoxy. The end result will be a completely waterproof deck, which will be completely sealed to the cabin with an epoxy layer. After that this part of the deck will be painted and treated with anti-slip inside the last layers of paint.