You can also go old school. Screw the eye into the balsa, then remove it. Then fill the hole with wood glue, and reinsert the eye. A more modern method along the same lines would be put some thin CA in the hole to harden it. Medium or Thick CA would glue the eye in, but I am not sure how well either would harden the balsa.
I agree with T-Rex:
"You can also go old school. Screw the eye into the balsa, then remove it. Then fill the hole with wood glue, and reinsert the eye."
I would recommend tying on the parachute on the shock cord, 1/3 the way down from the nose cone.
Shock cords supplied in kits are usually too short, you may want to get a longer elastic cord at a fabric store.
When the shock cord is tied at the nose cone screw eye, during recovery the nose cone flips in and out of the shroud lines and tangles up the parachute.
For me, on big or heavy cones, I prefer a hardwood plug or much longer hook eye (which normally uses a nut). My current build has a light cone and I used the glue method - screwed it in, took it out, added thin CA, wiped wood glue on the.threads and put it back.