Also imperialist leader in Europe might feel bold. Monarchs often took advantage of people when their down and cared more of expansion over common sense. For example, Britain and France is more aggressive with Venezuela or Mexico because they think US can’t say as much after losing war since they aren’t a “serious power” to them. They are ignorant and egotistical. A Wilhelm type monarch could easily feel more comfortable getting involved in Western Hemisphere. Every time US gets mad at Europeans fooling around in the Western Hemisphere the Europeans might call in the CSA as help.
With an independent Confederacy, European powers certainly would become more prone to intervening in the Western Hemisphere, but what makes you think the CSA would like that any more than the USA would?
Interest can easily change over time between countries. The more divided US the more Europeans think they can involve themselves here. A United US keeps them out better. CSA could have a easier time in Central America if Europeans are constantly getting involved in area trying to get control or set up plans for a canal you could see a power vacuum form in region after European interest fail money but the methods used in area might have left it very unstable and economic hardship which CSA takes advantage.
Without radical changes, both the US and Britain would oppose Confederate expansionism. The Confederates would also need to build a real navy. Latin American countries would not welcome the CSA - conquest would be slow and bloody even if it was usccessful. And tropical diseases would play havock with the Confederate invaders.