Either should work. I'm pretty sure the CA WOD has muscle snatches and stuff as minor assistance exercises, but I somewhat doubt that would be a problem. I mention the Mike's Gym WOD also because it may have some additional differences in the programming compared to the CA WOD. Likely nothing too critical besides the addition of metcon and thus slight reduction in lifting in the latter. I don't know of any article Mr. Burgener may have written like Greg's which explains his WOD, so you may have to ask the makers about any specific differences.
But like I said, there probably won't be any critical difference between the Mike's Gym WOD and the 4-week Bulgarian cycle of the CA WOD (shouldn't particularly matter which past cycle you grab). Since the Bulgarian cycle is more draining, it would likely be a good idea not to simply move from one such cycle to another, skipping the Strength. If you are going to be skipping the strength cycle, some extra time recovering between cycles may be necessary for the sake of injury avoidance.