Yeah, the SK has dowels sticking out near the top that are "chute snaggers", especially if ejection is past apogee.I vaguely remember an upscale satellite killer that had some spin issues with the chute on the way down, it got tangled in one of the panels
Re: the nose cone. You can leave it off like the SK. The design is so draggy there's no reason you need one. And not necessary to have the chute completely packed in to the tube. You can leave it sticking out the top. SK flies fine in that configuration.
Take the chute off and put on a nose cone when she's lying on the shelf. KISS.