Indeed, Nelson era first rate line of battle ships that hogged like bananas under the weight of iron plate armor were obviously transitional. It is useful to refer to the innovations that made every wooden hulled warship in the world obsolete.
No Nelson era first rate was armoured. The oldest RN ironclad to be armoured was laid down in 1849, converted to screw on the ways, launched in 1857 (and never commissioned owing to lack of need), and converted experimentally in 1862.
An 1850s screw liner is a very different beast from a "Nelson era" first rate, not least because it's about twice the size and has a powerful engine, along with having more guns with greater power. Comparing
Victory to
Duke of Wellington, the Victory had 102 guns averaging about 20 lbs per gun, the
Duke of Wellington had 131 guns averaging about 32 lbs per gun. The difference is pretty much a factor of two in weight of shot alone.
In 1824 a French 2 decker Pacificateur was decommissioned & used as a target. French General Henri-Joseph Paixhan's new anti ship explosive round received its baptismal proof of concept. His innovative shell was fused to penetrate the target & explode after a delay.
The assembled officers were stunned when the warship was reduced to a flaming inferno, broke up & sank after only a few rounds.
This description sounds like you're describing percussive fuzes (i.e. impact fuzes) with a delay on them. To my understanding explosive shells at this time were time fuzed, and it was innovations in the 1850s which led to the early impact fuzed shells - notably, for example, the US Navy didn't have impact fuzed shells in the Civil War. (The British used the Pillar fuze for Armstrong rifles and the Moorsom fuze for smoothbore shells.)
The description I've read of the Pacificateur firing doesn't sound like the ship was set on fire, broken up and destroyed by only a few rounds. The damage that's done in first hand accounts of the trials suggests that holes were made up to three feet on a side - certainly significant - but the only mention of incendiary effect is that it would have burned the ship if assistance had not been at hand.
In 1853 Russian & Turkish flotillas of (+/-) equal strength faced off at Sinop. Armed with Paixhan cannon & shells, the Russian ships lined up broadside to broadside in the time honored way. What followed was anything but traditional.
Eh? It wasn't an equal flotilla. The Russians brought six liners, two frigates and three steamers to attack an
anchored Turkish squadron (that wasn't ready for action) with nothing above a frigate; the Russians probably had at least twice as many guns.
ED: I've seen mention of the idea that the Turks actually set fire to their own ships, to prevent the Russians capturing them.
Every wooden warship in the world became obsolete at that moment.
Not really. Ships could endure long periods of bombardment in the Crimean War without being destroyed; witness HMS Agamemnon. She took 214 hits at Sevastopol and suffered 4 killed, 23 wounded.
What's going on here is that the explosive shell offers the opportunity for greater damage than a cannonball, assuming that the shell breaks through the sidewalls (which were very thick on a ship of the line, you can think of them as "woodclads" with up to three feet of wood as armour), but these are cannonballs with some gunpowder in them. They're not full of
high explosive like lyddite, and even lyddite shells just produced a lot of high velocity splinters.
The description you give of white-hot fragments igniting fires throughout sounds more like Martin's Shot, a British weapon of the late 1850s and early 1860s which had a filling of molten iron.