North Korea called itself a nuclear power on Monday, but the question now is whether U.S. President Donald Trump recognizes the rogue regime as one, a strategist told CNBC Tuesday.

That's an important development to watch as actions taken by Trump against North Korea will likely result in a cold war between the U.S. and China, said David Roche, president and global strategist at Independent Strategy. Such a turn of events between the two major powers would have global implications, he added, pointing to how it would affect worldwide trade and investment.

Outlining the two likely scenarios that could play out, Roche said the U.S. may try to contain North Korea by having "rings of missiles throughout the Asia Pacific region pointing at Pyongyang" or it could try to remove the hermit nation's leader Kim Jong Un through an attack.

Both those scenarios undermine China's influence — they would remove a key strategic ally from Beijing's foreign policy plan — and would lead to an "almost inevitable cold war" between China and the U.S., he said.