Get some 1/64" plywood and cut some strips from it. Make the first fairly wide (not knowing the diameter of the nose and the length, I can only guess at how wide), maybe about an inch or so. Epoxy it to the nose at the base, and then keep adding strips, but cutting them more narrow as you increase the diameter. Once you get the correct diameter, sand everything down so you get a smooth curve, rather than the "jaggie" look.
If it's a plastic nose cone, you might be better off using sheet styrene and CA, rather than plywood and epoxy, then give the entire area a layer of fiberglass to hold it all together.
You could also do a combination of the above, and sanding the front of the tube down a little.