If you are wondering if the halyard will hold your weight, and will the boat fall over when you get to the top...
The answer is "yes, if the halyard is in good condition" and "no it will not fall over."
IF you can get yourself into a good position up there to drill a straight hole, a battery drill will do the job, but do put a lanyard on this and any other tool you want to keep with you.
The tap will probably be a classic T handle one you turn with one hand.
You did not ask, and since we have no knowledge of your skill level with tools up there at the mast head, a possible Plan B might be to have the initial work done by a professional rigger while you take pictures, notes, and ask lots of questions. Then you will have a better idea of what to do when back in DIY mode.
Regards,
Loren