[Lev]

If shell modifier doesnt work for you, you can always do it manually -
1) Duplicate the cone and scale the copy down (Hold shift and scale)
2) Flip Normals on the new copy (should be either a separate modifier, or an option in edit mesh - not sure)
3) Attach two meshes together
4) Apply cap holes modifier to create links between the two pieces.

Still, shell modifier should be the fastest and easiest way. Why do you say it is not an option?