The game guide says the Orcs are the best blacksmiths. Does being an orc give any advantage in blacksmithing? Same for other races/skills

your right, and yes it's true to the lore. However, No, it is not listed in the racial trait. Unless it is a hidden trait not mentioned or noted.

Khajiit should get alchemy since they have such an interest in moonsugar/skooma.

Sort of, all races automatically start with their specific style unlocked - so an orc can start off making orcish armor, for example, or a khajiit could start off making khajiit armor. To get additional styles you have to find style books in the world to get the unlock.

Other than that, not really any difference between races as far as crafting goes.