We actually ended up removing every other mahogany strip to save some time and effort. However, I do not know if this was a good idea after all, since cleaning the area under the remaining strips was more difficult and took some additional time.
Now that the job is complete, I can say that it was definitely worth doing. So if you own a boat with a similar kind of structure, I think that it may be a good idea to remove first just a couple of strips to check, how the hidden surface looks behind the strips!
Before screwing back the strips, the top coat and wooden surfaces were wiped with some vinegar.