Soda blasting is to sand blasting as ballet is to break dancing. When you want to clean up something delicate where even glass beads would be harsh soda blasting is the way to go. It also has the advantage of being water soluble so that when you're done, rinsing the piece out with water will wash the soda away. This is good for all the small orifices on a carb that would be clogged with bead or sand.
Harbor Freight has soda blasters for $99.99 here.
Eastwood has a similar unit made in the USA for $409.99 here.
Unless you think you're going to be blasting away every weekend here is a do-it-yourself plan for making one out of common tools you probably already have. You could make one, try it out and then decide if it's good enough or whether you want to buy a more professional rig.