[Jim McDougall]

Just wanted to add:
After 1750s the British army brought emphasis on longer blades for the cavalry, which at this point were being inclined to combat from horseback in the European fashion. This broke from the characteristic 'dragoons', who actually used the horse as transportation primarily, and dismounted for action. Obviously this was the practice, outside incidental circumstances.

Blades for horsemen were increased to lengths ranging from 35 inches to 40 inches. I have seen M1788 heavy cavalry swords with such 40" blades, which are pretty imposing.

This example is a Glasgow type basket hilt for horsemen of the standing dragoon style units which remained in place as 'heavy' cavalry through the 18th century, even as 'light dragoon units' were evolving post 1760s.
This is believed of the form used by Royal Scots Greys (then Royal North British Dragoons) from then into 1770s.
Note the oval aperture in the hilt, which has now been agreed to have been for the horseman to secure his reins while discharging holster pistols.
Though these apertures have been regarded to have been from c.1750s, much earlier examples are known.

To the original query on the interesting sword shown in OP, I just wanted to illustrate that in character, the cavalry option appears unlikely. However, I might suggest there is even the potential this could be a private purchase, or ersatz version of a cutlass for naval use c.1800. British naval cutlasses of this period had straight blades of about this length. Naturally these areas are pretty clouded, and there are easily as many exceptions as there are norms, but wanted to present options.