As I understand a few European officers served on both sides, I think any practical experience was gratefully recieved.
Given Britain’s anti-slavery bias it is not impossible to envisage UK help, but the challenge is getting it early in the war when it is most needed. What the UK could have done was provide naval support early on, and training help to enable the North to build up the army more quickly and to a higher standard. As it was the UK sold large quantities of weapons to both sides, had they been sold solely to the North it might also have helped.
PODs might be no war of 1812, and closer economic links to the North rather than the South. Perhaps if the UK had more cotton sources in Egypt and India that would also help change the relationship.