Surely even the firebreathers would realise the utter pointlessness of war against both the American north (including Canada) and the Royal Navy? The Empire wouldn't even have to invade. They could just put on a trade embargo and the South's export economy would collapse.
You would think so, wouldn't you? However this is the same bunch that truly thought 'King Cotton' guaranteed them European support for their independence & retention of slavery in OTL.
TTL, they would probably try to court Spain (slave holding colonies) & France. Not realising/caring that post-revoltutionary/Napoleonic France is leaning towards the anti-slave lobby & that Spain is far too weak. They would also be arguing that any attempt to free the slaves violates the legal structure of the Empire, hence their secession from it. This, of course, would justify their actions in seizing (or trying to) seize RN assets.