It feels like it wouldn't really jibe with the lore to play as a race in a different alliance. Not that it could never be justified, but I highly doubt there's anything in the writing that might actually address the discrepancy, and it's probably just something you'd be expected to ignore. I'm sure a lot of people wouldn't have an issue with that, but if it were me, I'd just play as a member of my race's default alliance.
As for your race, I suggest you stick with the Orcs. You have a lot in common with them. They're big, green, have excessive elbows, are misunderstood by society, and live in strongholds.