No. I don’t believe there needs to be a constitutional amendment to allow the federal government to criminalize possession of nuclear weapons. The right to bear arms can be reasonably interpreted to apply to typical militia-style weapons that an individual soldier might carrier, not extending to tanks, howitzers, and nuclear bombs. If the SCOTUS actually ruled individuals had the right to possess chemical weapons, MOABs, etc., there WOULD be an amendment in short order...to ban said weapons.
If possession of a warship can legitimately be criminalized, then what would be the point of the Constitution authorizing Congress to issue letters of marque and reprisal?
The “crew-served” exemption offered by those squeamish about the Second Amendment doesn’t square with “shall not be infringed.”
As for privately-owned tanks: http://www.milvehtechfound.com/