I think you are right: adult rules would not be much fun for a seven year old.
I'd keep a realistic ground/ sea scale. It doesn't add to the complexity and would make it easier for him to graduate to an adult set if he wanted to.
Much as I like simultaneous movement for naval games I think you'd have to use I go: you go. Maybe have a random roll at the start of the bound to decide who goes first, in order not to make it too easy to set-up rams. Or the youngest of the players cd choose to move first or second?
Calculating realistic ram possibilities with turning circles would slow things too much. Perhaps only a ship with an enemy broadside athwart its bows at the start of the bound cd be allowed to attempt a ram. That would give the initial ramming advantage to a fleet in line abreast. It would also encourage him to think ahead in order to set-up ram possibilities. Success or failure cd be determined by an opposed dice roll, with the odds against success. Say, each roll a D6 with the rammer needing to double to succeed. If the target triples the attacker he's managed to get the enemy ahead of his bow. Ship cards give particularly manoeuvrable / awkward ships a plus or minus 1.
Idiosyncratic gun and armour schemes are the great joys of this period, but I think a seven year old would want a ship to have just one attack and one defence factor. Again, opposed dice would mean that he'd constantly have something to do. So a typical ironclad might have (say) a defence value of 6 and an attack value of 3. Each player wd add a D6 to that and if the shooter scores more he manages a significant penetrating hit.
People say that the chances of armour penetration have to made unrealistically high in the ironclad era in order to make more of a game. But what makes this period special is that it was really difficult (at least in the 1860s) to sink a first class ironclad with gunnery. I don't see that as a downer. It could be fun for a child to steam his Jules Verne style super ship (a Cerbčre, for example) through daddy's fleet with shot and shell bouncing harmlessly off her sides. The occasional successful hit on a formidable target would be something to celebrate. You cd maybe tip reality to the extent of making a 6:1 roll always a success. It wd be an early intro into the wargame habit of moaning about rolling 1s.
Once a significant penetrating hit had been achieved I don't think a child would want too much record keeping. Maybe a D6 roll – 1 speed halved; 2 or 3 reduce attack strength by one; 4 reduce defence strength by one; 5 damaged/ demoralised, must withdraw; 6 explodes.
If you allowed a standard ship to make two attack rolls – one afore and one abaft the beam – then a fleet in line ahead would have the advantage in a gun fight. Again, ship cards could cover special cases. Eg a single-turret monitor's low volume of fire cd give it just one dice, but bearing all round. While the long gun deck and negligible fore and aft fire of a Warrior cd be represented not allowing her to fire ahead or astern, but giving her an extra roll on the broadside.
I think a card per ship would be worthwhile. He'd discover just how individual these vessels were; and learn how to get the benefit out of them. You even cd jazz things up a bit – with round Russian ships spinning if they roll a 6; or each fleet cd have a captain particularly keen on gunnery, or a brave Buchanan, who steers towards the enemy regardless.
Sounds like a great project.