One of the main aftershocks could well be trade. The U.S. president does have a relatively large amount of discretion in trade. New agreements, such as the Trans-Pacific Partnership (TPP) and The Transatlantic Trade and Investment Partnership (TTIP), are likely to be halted.
However, these agreements were essentially political constructs that were primarily designed to benefit the U.S. and those nations that allied themselves to the U.S. at the expense of others. The TPP has already started to divide Asia into those who benefit most from TPP (e.g. Vietnam) and those who don't (e.g. China and Thailand). Trump is basically moving those battle lines but I don't see these fractures as being worse. In fact, a better outcome for China may even delay global and regional instability. Similarly, Trump will no doubt cut the TTIP.
A Trump trade war with China is likely to be no more damaging and arguably less damaging and less effective (but much clumsier, more visible and playing to the gallery) than the TPP would have been for China. Ultimately this may be a zero-sum game but a zero-sum game where China can't afford to lose without there being potentially serious consequences for the Chinese and global economy. For this reason, Trump barging noisily through the front door may prove less of an immediate trigger to a Chinese depression than TPP more subtly attacking China via the backdoor, like a stealthy cat burglar.
Trump has stated that he would renegotiate NAFTA (North American Free Trade Agreement) and potentially withdraw the U.S. from the agreement if consensus with other members could not been found. He would not need congressional approval to do this; although this is not saying he would. Trump will likely come under pressure to give details of his plans, particularly as the Mexican peso drops significantly in value.