You'll have a difficult time using a drill bit to move a hole if it still mostly overlaps the original. In a rigid setup like a milling machine it sometimes works if the drill is short/stiff, but freehand will be quite difficult if it even works. That's why my first choice would be a milling machine with end mill.

Grigg

•1951 GMC 250 in the Project Journals
•1948 Chevrolet 6400 - Detroit Diesel 4-53T - Roadranger 10 speed overdrive - 4 wheel disc brakes
•1952 Chevrolet 3800 pickup
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"First, get a clear notion of what you desire to accomplish, and then in all probability you will succeed in doing it..." -Henry Maudslay-