No need for any drilling, the hub studs are pressed in from the rear on splines.
You should be able to use a hammer and a 6-8mm punch to drive the broken stud out from the wheel side, then knock a replacement in from the rear. The biggest problem is that you have to remove and insert the new bolt from the rear of the hub.
Is it a front or rear hub?
If it's a rear hub, it's easy enough - removing the complete hub takes a few minutes after removing the brake caliper and disk, and the job can be done on the bench.
If it's a front hub, I suspect that if you remove the brake caliper and disk, there will be just enough room to squeeze a new bolt in where the caliper sits, without removing the hub. You will have to flatten the lip of the brake disc shield towards the centre of the car and straighten it back afterwards. Just tap the new bolt into the hub from the rear, and pull fully home with the wheel nut after replacing the wheel. You may have to file a bit of a flat on the mushroom head to get it in past the hub carrier, or you may not - it depends how your luck is.
You really don't want to be removing the front hub if you can help it, it's a biggish job and you would have to replace the wheel bearing too, as it will be damaged whilst removing the hub.
You should get a new bolt for under £5, as Jocko says.