I'd recommend opening the player and removing the top lid, then drilling your hole in the lid with it removed from the player (after carefully marking the desired location). That way you don't get any shavings inside the unit.

...or you could simply use the threaded M5 insert in the back of the unit through the sled to lock the unit in, thereby avoiding having to drill at all....

One of the few remaining Mk1 owners... #00015