I doesn't really have to be the Han dynasty. How would a Qi-unified China which is more focused on the east (producing continent-sized butterflies) fare? More eastwards expansion and a stronger Chinese navy?
I might be wrong here, but didn't Japan really start to be influenced by China after the Han?
Qi was one of the stronger kingdoms in the Warring States period, but unifying under them would be a much longer prospect than the Qin. Jin was the strongest state for a little while, but it was broken apart into three states. Qin was the next best prospect. Chu had a decent shot, but it was a victim of its own size so it could not conquer without risking invasion from its other fronts. Qi was densely populated, rich, and an early sponsor for Legalism, but otherwise it was more of a deciding factor in alliance systems rather than a state with a real shot of being the main unifier.
Japan had indirect influence from China for many centuries, with some influence before the Han being suggested, but Japan only truly got the notice of China in the Three Kingdoms era - and would only be truly influenced during the Northern and Southern Dynastic period. This influence peaked under the Tang, and then Japan started to project its own identity within the umbrella of Chinese civilization. Another important factor to bring up is that Japan was fragmentary, more village and principality, than a state around this time period. It was only around the time of the Tang that Japan was emerging as a cohesive force, suggesting that Chinese influence was most prominent at the time period where Japan was in its early emergence as a unified state.