Denny, I was thinking about your earlier comment that you'd just snip the hole out with your shears. I wondered if you'd give it a try and post pictures as you're known to do. I see now that you don't disappoint!
I too thought about that but remember that the OP claims the sheet metal is 1/16" which is about 16 gauge. Last week I was doing some straight cuts in 16 ga with some nice aviation snips and it's real work. I have not tried cutting a 4" circle in 16 ga sheet but I think it'd be quite difficult. Much more difficult than thin more or less flexible sheet metal like you showed.
In the end though there are several good ways to accomplish the task, the best method will suit the individual's ability, tool box, and budget.
Grigg