At last a subject that is my hobby !!
Until a few years ago we used to have an annual clay shoot on the Stena Sealink from Fishguard to Rosslare. All shooting took place over the stern and it was an excellent day. Difficulties finally arose with graeter controls on guns with 30 of us boarding a passenger boat. And for those who have never shot from a moving boat then rest assured it is damned hard !
However there were no legal issues and I understand this is still the case. Indeed boats are used in some parts of the country for wildfowling eg. the Broads punts.
There may be an issue if using a propelled vehicle for game if the same law applies as does on land.
Apart from safety issues and taking into account environmental concerns, byelaws and the quiet right of others I can see no reason why clay shooting cant happen on a boat. Quite common on big powered yachts.
Indeed I have looked at mounting one of our automatic traps on a 10m RHIB just for a bit of fun. Never got there due to time etc. Also thought of paintballing with a few big RHIBs !!.. now theres a good corporate day ! To this end have purchased a couple of professional paintball kits for the kids for xmas, but secretly part of some R&D!