I wouldn't poke holes in the parachute. Typically we've seen people use the following approaches, both of which work well:
Get a parachute with a loop on the canopy so that the balloon gets tied to the top and the “payload train” gets tied beneath the parachute. I forget if the rocketman parachutes have this or not.
If you do not have a parachute with an attachment loop on the top of the canopy, you can make do by connecting the bottom of the balloon and the top of the “payload train” to the bottom of the parachute. In this way, on ascent, the parachute drags along not moving fast enough to inflate.
