A nose cone? Any Iranian with a hammer and a sheet of metal can beat a nose cone into some shape in an afternoon.
Yes, but that would cause...ahem...delivery problems.
Nuclear weapons aren't like conventional explosives. For one thing, the radiation *from* the nuclear warhead can...mmmm...interfere with volatile rocket fuels...electronics...etc.
For another thing, vibrations from the rocket can crack the hyper-brittle heavy metals that comprise the physics package...and such vibrations can also interfere with the precise shapes involved.
Rocket-fuel fumes can likewise be problematic if they reach any of several nuclear weapon components.
These are non-trivial technical hurdles.