I had the good fortune to serve as a guide on HMS Victory in the early 80's - Tis true he was carried below to the Orlop Deck (The 1st deck below the waterline) The deck of the orlop was always painted red in any ship as that was where the 'Sawbones' would perform his operations/amputations.
Nelson taken to a part of the orlaop called the 'cockpit' and was leaned against the ship's 'knee' (a sort of bracing) and administered to but died some 4 hours after being shot through - He apparently drown in his own blood rather that succumbing to the actual lead shot (although it certainly was a deciding factor)
Captain Hardy was one of the tallest men on board at the time (approx 6ft tall) and in the famous painting of Nelson's death he can be seen standing upright to Nelson's left with his right hand on the bulkhead (wall)
I am 5'10" and I had to crouch when in the 'holy of holies' as it was known. The artist used quite a bit of license when making his sketches once the 'Victory' returned to England - In the picture there are 16 people including Nelson
Apparently the only people who were actually there at the 'end' were the surgeon, one of his assistants and Captain Hardy (and possibly the Ship's Chaplain but this is not verified)