About the question whether the 2nd Bataillon of the Dutch Legion of Orange was armed when it marched to Holland...
In the Dutch National Archives there is a Report of General Schwartz, dated 12th January 1814 (2.13.01 invent.nr. 11, minute of 31st January 1814, Nr 8.)
He informs the War Department that the 2nd Baaillon and a Detachment of Artillery will leave for Holland on the 18th. He says - and I quote:
"Het Batt is gewapend and gekleed" or: the bataillon is armed and clothed. Then he itemizes what's missing and that doesn't include weapons.
According to a later Inspection Report in 1816 the bataillon still uses British style brush and prickers instead of the French style chain and pricker adopted in 1814. They must have been issued these in Germany. They certainly did not recieve them from Dutch stores. Their sergeants still used British style swords too.
That proves - I think - that you were wrong to think that the British did not supply arms to the Dutch troops in Germany.