If you'll excuse the slight ignorance, I'd suggest that the only useful sediments are those which are considerably older and thus compacted.
The history of the Menai Strait has been refined recently through the use of a jack-up drilling rig to take core samples - a commercial rate for such a device is about £20,000 per week, so it's utterly pointless to suggest that no bit of seabed should be disturbed just in case someone wants to investigate the sediments.
Digging up bits of seabed to remove wrecks is a perfectly justifiable operation as there is plenty of similar seabed around them, the vast, vast majority of which will never be of interest to anyone.
Now then, back on topic. :)
Does anyone know anything about the slate ship found off Pwll Fanog on the Menai Strait, which has slates from Llanberis which were quarried in the 14th or 15th Century...?
Hello again darkness, my old friend...