OK... Instructor hat on.
We MSF Ridercoaches teach the swerve as two quick countersteer operations, with your torso upright. Let the bike roll around under you and do not try to lean with the bike as it will slow the roll rate. Separate the braking, if any, from the swerving simply because if you do the two quick countersteer maneuvers correctly you will be using essentially all the available traction getting the bike around the problem. If you attempt braking you will almost guarantee a low-side crash when a wheel locks up.
If you attempt to pull in the clutch lever when doing this, you will destabilize the suspension of the motorcycle and probably end up hitting the object your are trying to avoid.
A better survival plan is to keep enough space - the "space cushion" (a reactionary gap ) between yourself and anything in front of you so you do not have to execute a swerve as an emergency maneuver. No tailgating ever !, and keep your head on a swivel to avoid problems in the first place.
While we are on the topic of swerving, how many of you actually practice that regularly ? It is one of three emergency maneuvers that are volatile skills that you will lose if not practiced.
The other two are emergency stops straight ahead, and emergency stops in curves, both left and right.
How many of you with ABS brakes actually know what they do on your bike ? Go out and do a few quick stops and see how the ABS reacts. You really need to know the capabilities.
Please consider taking a MSF course as a refresher, Basic Ridercourse, Basic Ridercourse 2, or the new Advanced Rider Course. You will have a fun time doing the exercises, and might learn something. I have had many riders take refresher courses over the years and they all say they either learned something new, or corrected bad habits they had gotten into over time.
The absolutely best feedback we receive is when former students come to visit us at class or see us on the road and tell us that something they learned in class saved a bad crash. That makes it worth all the blazing hot days we stand out on the range dodging motorcycles. That is priceless.
Ride safe out there and remember: You are invisible and everyone is out to kill you. Act accordingly.