It is more likely that there will be occasional bumps along the road, and some of them could be pretty big. In the near term, were the US slowdown to become deeper and more protracted, Asia would probably be affected. It is true that direct trade linkages with the US have become relatively smaller as a share of total Asian trade in recent years.
But while a larger share of Asian exports is now going to China, most of this trade is just part of the regional chain producing final goods for sale outside of the region in the major countries, a big part of which is still accounted for by the US.