16 gauge is 1/16" but that's a coincidence, gauge and thickness numbers don't correlate.
Forget about a flycutter if you only have a hand drill.
With your tools I'd try the hole saw and cutting oil. If you cheap out on the hole saw it may not last the first hole.
If you do try this, make sure the work is securely fastened because it will grab hard and spin if it gets a chance.
Also, use a radial handle on the drill or it'll try to break your wrist when it grabs.
Sheet metal is dangerous to work with so you need to be prepared.
So far, everything that has surprised me has been completely unexpected.