Hello Saskia and welcome to the forum. I am not certain from your photos that they are all wood because Cacite can form fibrous lumps called 'beef'. I would need to see the detail using a hand lens or microscope.
Whatever you have needs to have any salt from the sea water removed as this can break up the specimen when dry. Soak them in a bucket of tap water for a week or so changing the water every couple of days and giving them a scrub with a toothbrush to remove any loose particles. Allow to dry out naturally. This should then be all that is needed unless there is evidence of Iron Pyrites (crystals,within the structure of the rocks. If you see a whitish powder forming then this is Pyrite decay and will need special treatment. I hope this helps!
Thank you! Will give it a go and see what (if anything) comes of it 🙂