The similar picture which I supplied in my earlier reply above was from Robson 'Swords of the British Army' . So I would ID this as a Cavalry Levee sword rather than a band sword and so would go with the 18th as being the 18th Light Dragoons 1763 ( which became the 18th Royal Hussars (Queen Mary's Own) in 1910 ) .
The entry relating to this regiment in Hallows excellent book ...