[Jim McDougall]

It seems to me that in all the entries I have found, these flintlock pistols with the 'rounded off' terminus of the stock void of ramrod attachment, are stated 'Belgian sea service' . In some cases they are noted as Dutch.
Whatever the case, they were apparently produced in considerable volume and as I noted earlier, England was a key client in supplying her navy.

Most of the examples are dated from 1800-1820, and are described by well regarded dealers and auctions.

This is an interesting discussion on the dynamics of combat in which these were used and why the absence of ramrod. The purpose of these pistols was to create havoc and injuries amidst a mass of opponents, much as with the blunderbusses and deck guns.
This was the reason for the heft and large bore barrels, effectively 'scatter gun' tactics. These were most likely loaded with 'buck and ball', that is varying dimension shot, or whatever ball was available to create a barrage in a single shot (as Mark well describes as partridge shot).

Just as in a cavalry charge, once the gun was spent, it became either a bludgeon or was released. As with cavalry, these weapons would be better kept than lost so the lanyard was intended to keep the gun at hand, not inaccessible or lost overboard.

As Will has mentioned, the idea of reloading in haste or in a charge or melee is typically doomed to disaster. Also as he notes, in excessive movement etc. the ramrod could be lost, which is why later there were swivels designed that kept them attached on many percussion guns.

A very salient point Mark brings up, private purchase, as with merchant vessels would be exempt from many required markings.

Attached several other examples of 'Belgian Sea Service' pistols, in one instance in a pair, hence 'two shots' (a la' Blackbeard with his 'brace' of 'Queen Anne's'. ).

An analogy: my Caucasian percussion pistol, note the large ball butt for use as a bludgeon, the lanyard, and noticeably, no ramrod.
This was likely made in Liege as well.