I think I see the problem. You have no idea what the Declaration of Neutrality issued by the UK in May, 1861, says. It does not address small arms, but specifically address the building and equipping of warships. Here is the applicable text:
"That if any person, within any part of the United Kingdom, or in any part of His Majesty's dominions beyond the seas, shall, without the leave and license of His Majesty for that purpose first had and obtained as aforesaid, equip, furnish, fit out, or arm, or attempt or endeavor to equip, furnish, fit out, or arm, or procure to be equipped, furnished, fitted out, or armed, or shall knowingly aid, assist, or be concerned in the equipping, furnishing, fitting out, or arming of any ship or vessel, with intent or in order that such ship or vessel shall be employed in the service of any foreign prince, State or potentate, or of any foreign colony, province, or part of any province or people, or of any person or persons exercising or assuming to exercise, any powers of government in or over any foreign State, colony, province, or part of any province or people, as a transport or store ship, or with intent to cruise or commit hostilities against any prince, State or potentate, or against the subjects or citizens of any prince, State, or potentate, or against the persons exercising or assuming to exercise the powers of government in any colony, province, or part of any province or country, or against the inhabitants of any foreign colony province, or part of any province or country, with whom His Majesty shall not then be at war; or shall, within the United Kingdom, or any of His Majesty's dominions, or in any settlement, colony, territory, island, or place belonging or subject to His Majesty, issue or deliver any commission for any ship or vessel, to the intent that such ship or vessel shall be employed as aforesaid, every such person so offending shall be deemed guilty of a misdemeanor, and shall upon conviction thereof, upon any information or indictment, be punished by fine and imprisonment, or either of them, at the discretion of the Court in which such offender shall be convicted; and every such ship or vessel, with the tackle, apparel, and furniture, together with all the materials, arms, ammunition, and stores which may belong to or be on board of any such ship or vessel, shall be forfeited; and it shall be lawful for any officer of His Majesty's Customs or Excise, or any officer of His Majesty's navy, who is by law empowered to make seizures, for any forfeiture incurred under any of the laws of Customs or Excise, or the laws of trade and navigation, to seize such ships and vessels aforesaid, and in such places and in such manner in which the officers of His Majesty's Customs or Excise and the officers of His Majesty's navy are empowered respectively to make seizures under the laws of Customs and Excise, or under the laws of trade and navigation; and that every ship and vessel, with the tackle, apparel, and furniture, together with all the materials, arms, ammunition and stores which may belong to or be on board of such ship or vessel, may be prosecuted and condemned in the like manner, and in such courts as ships or vessels may be prosecuted and condemned for any breach of the laws made for the protection of the revenues of Customs and Excise, or of the laws of trade and navigation.
And it is in and by the said act further enacted --
"That if any person in any part of the United Kingdom of Great Britain and Ireland, or in any part of His Majesty's dominions beyond the seas, without leave and license of His Majesty for that purpose first had and obtained as aforesaid, shall, by adding to the number of the guns of such vessel, or by changing those on board for other guns, or by the addition of any equipment for war, increase or augment, or procure to be increased or augmented, or shall be knowingly concerned in increasing or augmenting the warlike force of any ship or vessel of war or cruiser, or other armed vessel, which at the time of her arrival in any part of the United Kingdom, or any of His Majesty's dominions, was a ship of war, cruiser, or armed vessel in the service of any foreign Prince, State, or Potentate, or of any person or persons exercising or assuming to exercise any powers of government in or over any colony, province, or part of any province or people belonging to the subjects of any such Prince, State, or Potentate, or to the inhabitants of any colony, province, or part of any province or country under the control of any person or persons so exercising or assuming to exercise the powers of Government, every such person so offending shall be deemed guilty of a misdemeanor, and shall, upon being convicted thereof, upon any information or indictment, be punished by fine and imprisonment, or either of them, at the discretion of the Court before which such offender shall be convicted."
"Now, in order that none of our subjects may unwarily render themselves liable to the penalties imposed by the said statute, we do hereby strictly command, that no person or persons whatsoever do commit any act, matter or thing whatsoever, contrary to the provisions of the said statute, upon pain of the several penalties by the said statute imposed, and of our high displeasure."
It was the violation of this proclamation that gave rise to the Alabama claims. The arbitrators found that the UK had knowledge that this was happening (primarily because US agents told them it was happening), and the UK did not exercise due diligence to enforce its own laws.