Rather than use a vice to hold the figure I’m drilling, I use blutack. Big blob of the stuff.
I’ve drilled the hands of 100s of Peter Pig lowland pikemen out (annoyingly the only pikemen in their range not available open handed). Still got all my own fingers.
Blutack is brilliant. Wrap the figure in the middle of the blob. Push it down onto the cutting mat, for extra security hold in place with your fingers. Blutack provides a buffer zone between fingers/figure/sharp thing if there is a slip. You can angle figures to drill at strange angles. If you need to hold the figure to drill, still wrap in blutack – if you are drilling a number of figures you’ll find hanging on to figures is hard going on the fingers, blutack provides a welcome cushion.
My other top tip is don’t forget a pilot hole – I use a long RC fuel line cleaning needle thing.
You may find that drilling/cutting/filing a groove is a lot easier (and much less stressful).