If you use a drive screw that is too large you will dimple the head tube. Please don't ask me how I learned this.
I have been able to work around the the lack of punches with a cupped face as noted by @repechage by using a large carpentry nail set. They are made with cupped faces to hold finishing nails in place when setting them.
Brent

I've had good luck using drive screws in the past. I usually put a little blue Loctite on the threads and then tap them into place. They should be carefully checked to make sure they are the correct size for the hole before tapping them in. Otherwise, they've worked well for me and look fine.

I used these on my 1958 Raleigh