In a case like that, it would be wrong to ignore the invitation, but formal regrets sent to the Captain would cover you completely.
Sorry, but you need to review the subtle points of maritme etiquette. Sending regrets to the master while embarked aboard his (or her) vessel is indeed a major faux pas -- just like sending regrets to a head of state (one may not, for example, decline an invitation from the President of the United States). More precisely, one may decline an invitation from the master of a vessel, while embarked therein, only to accept an invitation from a head of state. In fact, the rules of etiquette demand that one withdraw a previous acceptance of another invitation if one receives a conflicting invitation from the master of the vessel.
The fact that nobody may notice your failure to attend the Captain's "Welcome Aboard" Cocktail Party, or some similar event, does not mean that such a failure is not a major breach of etiquette. Rather, the lack of "RSVP" on the invitation reflects a presumption that one will accept the invitation because the rules of maritime etiquette do not permit one to do otherwise.