You can place some sticky tape on the far side of the panel to catch most or all of what falls that way. Just tent it a little. Other things, like Silly Putty, or modeling clay can work as well.
If you use a sharp bit, with lube, the cut will be clean and the shavings will tend to cling to the lube. Use good technique, modulate the pressure so that short spirals are formed and break off (on the outside!).
Strategic placement of cardboard or paper over circuitry to redirect shavings can give you added confidence. Tape in place if required
When you finish, compressed air, a shop vac, and a paint brush can all help to make sure nothing remains.
