I doubt that.
This is closer to what was used in 1805
That's a fantasy uniform. Only officers' full dress retained that cut in the 1795 regulations, the undress uniform was cut as seen in NW, and it lacks the lacing of full dress. By 1800, however, the undress cut had been effectively adopted universally for the full dress coat. This is confirmed by by contemporary images, such as this
1804 portrait of Sir Edward Pellew. This
1806 painting of the death of Nelson shows all officers except Nelson and a lieutenant on the weather deck in the cut seen in NW. This
1807 painting shows a similar situation. And of course there is this
1807 portrait of Captain Tom Foley that the NW uniform is surely based on.
Or take this
1806 portrait of Captain Peter Rainier, or this
1802 portrait of Captain Samuel Linzee or any of the several dozen other images I can provide. There may not have been any official changes to the uniforms between 1795 and 1812, but they unquestionably did change.
That museum piece is the regulation 1795 full dress coat, but as Hood died in 1798, he wouldn't have had a chance to adopt the later style that had become the standard by Trafalgar.
You're more than welcome to make the uniform how ever you please, but it won't be accurate for 1805.