@ThreeJsDad That is indeed a simple and proven system. If I may suggest, don't rely on the quality of the cutting edge from grinding a hole because when the charge goes off, there will be a shockwave that could momentarily change the dimensions of your tubes and you could end up with the cutting edges misaligned (like a pair of scissors with a loose joint in the middle so the blades are separated a short distance and whatever you're cutting just flops between the blades). Honestly, if you run the cord through the tubes right alongside the Christmas bulb, the blast alone should be able to sever the cord just from the heat and pressure. If testing proves otherwise, you could also try incorporating an X-Acto knife blade to act like a guillotine to cut the cord as the tubes separate.
Also, if you use this method of cord cutting, be sure to consider potential damage to your parachute. If the tubes with the Christmas bulb are alongside the parachute bundle, you run the risk of burning the canopy. If you want to go with that arrangement, maybe having a nomex blanket wrapped around the parachute or a deployment bag would be ideal.