My first cardstock model build was the Bob Harrington template for the Satellite Interceptor, yes it has that nose cone. It was a very challenging nose cone for a beginner. Now, I simply truncate the tip slightly so I have a small open dia where I can grab the glue tab with tweezers or use a skewer to help close up the glue joint at the tab, and then fill in the tip later with a drop of glue or a piece of balsa that I can sand to conform to the pointy nose cone shape, or just leave the little flat part.
I got a little better at it, but still tricky to get them even, with this Nike Smoke, I put a little dowel in the open hole at the tip.
The Dr. Zooch witch hats on the Soyuz boosters at least have a seam that you can hide when you glue them to the core stage.
That is a cool model, where did you find the template? - never mind I see the link on your other thread.