All things considered, a career on the nationalist wing of the Labour party isn't that out there (and yes, believe it or not, such a wing does exist). The First Minister did go through a period on the comparatively hard-left of the SNP. In terms of his personal politics and ethos, there isn't just too much to distinguish Alex Salmond from any of Labour's recent leaders. A bit to the left, maybe.
On the other hand, there's a lot in nationalist thinking that's fairly conservative in its general ethos. The idea of a country being essentially self-reliant is a thoroughly conservative concept, as is the idea of saving the tax from one's natural resources rather than pissing it against a wall.
Supposing Mr Salmond had fallen in with a different crowd during his youth or his time at university, there's a possibility that he might have ended up a Tory, of the One Nation variety.
To be honest, though, I think he's far more likely to end up in Labour. They have the electoral machinery where he was brought up, and their ideology chimes closer to what Alex Salmond is. Inside that party, he'd be sure to rise quickly. It's a push to get him as PM, but frankly, knowing the First Minister's capacity for the quick shoe-shuffle, nothing would be out of the question.
One thing he'd always be is a Scottish nationalist with a little 'n', whatever party he'd ended up in. Everything about his upbringing pushed him that way. Whether he'd have plumped for devolution, or maybe full fiscal autonomy, I can't forsee any scenario where he would stand up and pooh-pooh Scotland quite as enthusiastically as some of his opponents are capable of in OTL.
Indeed, that ingrained nationalism might wind up with him back in Scotland and not PM anyway, as leader of Labour or the Tories in the Scottish Parliament, assuming such a thing had been established without him.