I don't know how finicky a briggs is going to be about balance, but...if your going to balance the flywheel. You need to find the heavy spots and either remove weight, or add weight opposite, to balance it. It proved difficult to type up a description of how to make your own balancing stand...so, just search for motorcycle wheel balancer or flyweel balancer and you will get the idea. The ones I saw all showed two mounted bearings per side with the axle riding on top...you only need one precision bearing per side ON the axle...and have the bearings rest in the square tubing of the stand...cheap and easy.
If your just shaving the fins (assuming machining)...that really shouldn't effect the balance. If you are removing them in a more improvised way (hacking
)...then all bets are off.
As to cooling, I don't know. I would assume you would be good as long as you don't let it run static for lengthy periods.
Jason