Oh no, thou hath summoned the Spanish Nitpicker!
We discussed this before when adding Carlos IV as king pre-1808, but I would still argue that for the post-1808 part of the period maybe Joseph Bonaparte should be switched for Fernando VII, and Spain made to be at war with France and allied with Britain from 1808 onwards (that wouldn't affect the Hornblower storyline, it would be like other historical relation changes set within periods, right?). Joseph Bonaparte never had any control over the colonies and the colonial authorities (those that didn't declare independence*) recognized Fernando VII as king and governed in his name. Therefore they would keep the Bourbon coat of arms (although I agree the flags are more recognizable at that resolution and should probably be kept for clarity's sake).
Now, I realize that if we were to open that can of worms, we probably should also change Napoleon for Louis XVIII and end the war in 1815, include the war of 1812 between Britain and the US, etc. And if we did that in the Napoleonic period, we should do it with the rest and that would be a giant mess to sort. But if we were to experiment with it, the Napoleonic period being one of the shortest and less packed with storylines and whatnot, would probably be a good place to start. For the rest of the periods, changing the names of the kings as time goes by would be enough, no need to add every tiny change of relations, we have already enough of those set already.
*Actually, it could be interesting to apply the new nation template of Sweden to maybe do something similar with the Spanish American independence movements from say 1810 onwards, to spice up the late Napoleonic period. Like spawning Colombian privateers (they didn't have a proper navy, so it would be mostly schooners and brigs), or even giving them the city of Cartagena, which was one of the first to declare independence. It would be interesting for characters like Jean Laffite who did have a Colombian letter of marque at some point in his career.
There's a lot in this post and almost nothing relevant to the topic at hand. Sorry, I kept thinking stuff up as I went and got carried away.