I'm curious as to how you guys handle going through an intersection that has a right turn only lane?

If it's red, I will try to get into the next lane to go straight, but I've recently had a few problems with cars that will stop in the right turn only lane, only to continue on straight, honking at me like I'm in the wrong? I always check before getting back over to the right side after the intersection but it's an unsettling situation to be stuck between two moving cars.

Is this the correct way to proceed through an intersection with a right turn only lane? Or should I just stay to the right and straddle the crosswalk through?