The US Army has been teaching people to exhale slightly all the way through the trigger break, rather than to hold your breath. When you are exhaling, it is harder for your muscles to tighten up and flinch. Also, in the off hand position, just as the trigger break is starting, to lean slightly forward in a gentle motion toward the target as the break is occurring. This is sort of like a gyroscopic stabilizer. When you are moving in a direction, it is harder to disrupt the momentum, which is aided or modified by gravity with a lateral force (your side to side wobble), and the east-west component has a slight tendency to tighten up.
This brings up the subject of action speed and barrel dwell time and technique. If you shoot a lot of position rimfire or centerfire, the total elapsed dwell time is going to be in the .010 range. If you shoot flinters, the total elapsed time might be .100 seconds. So lets take an average shooter, with a 7 ring to 7 ring offhand wobble. In faster locked guns they may have learned to time their trigger break to let the shot go just as the sights are crossing the 9 ring to enter the 10 ring. The result is a 10. If the shooter uses the same trigger break timing with a flinter, the longer dwell time won't exit the ball until the wobble is well past the 10, and may result in a shot well outside the 7 on the other side. (Remember, there is the momentum of the direction of the wobble going on here too.) So, a significant difference in trigger break timing is needed to shoot a flinter as well.
One other thing about wobble and position. Unlike being all viced in and slung up tightly in prone position, where your pulse as transmitted through the sling controls the direction of the wobble, in the unsupported standing position it is seldom consistent in one direction. Until the direction is established, you really don't know that it's going to cross the 10 ring. Some times it may move from 4 o'clock to 8 o'clock and not cross the 10 ring, or be otherwise random. I personally feel best in making my trigger break when the wobble is moving upwards from 6 o'clock toward the 10 ring in timing my trigger break, but others may feel differently. So, each action type is different, and each gun is different. The trick is to get to know each gun (and your own abilities in position with it) in order to shoot it well consistently.