But privateers are not cluster bombs. The USA for much of its early years did not believe in maintaining a huge army or navy. Privateers were a way of conducting economic warfare against countries with huge navies.
Which makes it a bit odd that 55 nations signed it, including many with navies far smaller than the American one. My point in bringing up cluster bombs is that they're a way of fighting war which was considered to have too much chance for unnecessary harm to neutral parties; the same can be said of land mines, and indeed things like biological and chemical weapons.
Considering that the British were still divvying up prizes on their Navy ships well into the 20th century, I don't they can protest too much about privateers.
The overall conclusion of much of Europe at the time was that privateers could not be kept under proper control; the agreement grew out of one between Britain and France (allies in the Crimean War) not to issue letters of marque during that war. For controllability there is a great difference between an official commissioned Navy ship under an officer and subject to discipline, and a privately owned ship operating without any formal control structures.
For a reasonable proof that the attitude of the British Government was significantly influenced by the US asking about outfitting privateers (which, I'll remind you, was your claim), we would need to have some binary examples. Specifically we would need an example or examples of where evidence was brought in a case
before this US initiative where the evidence did
not lead to action being taken (or orders for same).
In the case of the Alabama specifically, for example, we have:
The customs commissioners (who inspected Hull 290 a week after Adam's initial request) did not find something that could be described as "warlike stores".
The Queen's Advocate, Sir John Dorney Harding, suffered a nervous breakdown and was unable to reply directly to Adams' second, more conclusive letter. The Advocate General only sees it on the evening of the 28th July, and orders are promptly issued for the ship to be seized.
Bulloch's spy network, however, informed him on the 26th July that the ship was about to be seized. He was thus able to sail on the 29th, and barely evaded seizure.
None of this looks like the British being reluctant to act, and therefore we cannot use their acting
after the privateer saber-rattling to prove that the privateer saber-rattling was necessary.
Of course, it's certainly possible that Seward thought it was necessary; he seems to have been at best quite ill informed on international law. For example in 1861 he argued that Britain should officially declare that belligerents not be allowed to linger for more than a few days in ports, on the grounds that otherwise Britain would be the only exception to such a rule in Europe; as it happens, the French rules were far more lax and the
Alabama was allowed to linger in a French port for months on end.