What have happened :
Outside their frozen homeland, Chukotko-Kamchatkan peoples have had little impact upon world history.Numbering a few ten of thousands at best, they fished and herded reindeer in the north-eastern reaches of Siberia until discovered by the Russian during the XVIIth century. The Chukchee proved a tough nut to crack, defeating several expeditions and forcing the closure of the Anadyrsk fort, but were ultimately incorporated into the Russian then Soviet Empire. They still speak their language and still herd reindeers, and are the subjects of somewhat two-edged Russian jokes, but if we set aside the buterflies, they have little impact upon world affairs.
What might have happened :
We dont't know much about the prehistory of north-eastern Asia. The bulk of the population was apparently tungusig in the South and Chukotko-Kamchatkan in the north, while some form of Japonic dominated in Korea. Relict populations speaking now extinct languages probably survived in the Amur region - their only modern descendant being the Nivkhs. Nomadic confederations controled the western steppes, while Mandchuria was disputed between Chinese states (first the kingdom of Yan, then the Qin and Han Empires) and the states founded by the Buyeo peoples, an extinct group which spoke a language akin to Japanese and which seems to have originated from a non-chinese fishing culture on the coast of the Yellow Sea.
Migration of small tribes were relatively common place at the time, and could have huge consequences. The Japanese, for instance, were the descendants of fishermen from the Yellow Sea who had sailed east to flee Chinese encroachments. Around 300 BC a small Chukotko-Kamchatkan group - no more than 500 persons in all - are forced to leave their frozen homeland by tribal wars. They head south-weast and by 203 BCE they reached the territory of the Xiong-Nu confederation.
The Xiong-Nu elite was Yenisseian speaking, but their subjects were of mixed ethnicity, with proto-turkic or proto-mongolic tribes. The newcommers were quickly integrated into the Xiong-Nu power structure as the Raven clan (Chinese 烏鴉 ) and settled in the Ordos region. They adopted the nomadic lifestyle but kept their language and religion. They were quite low in the internal Xiong-Nu hierarchy and tended not to attract much attention but they fought in the Xiong-Nu armies against the Han in the Xiong-Nu - Han wars and participated in raids into Buyeo and Koguryo territory.
The impact at this point is still limited; A few Chinese or Koguryo soldiers who would have lived in our timeline are killed by Raven arrows. This will have a major effect later, but for the moment, only their families notice.
In 60 BC the Xiong-Nu Empire was shattered by a civil war as the throne was usurped by Woyanqudi, a grandson of the 12th Chanyu's cousin. Huhanye, the son of the late Chanyu revolted, driving the usurper to defeat then suicide but couldn't quite assert his authority. His brother claimed the kingship, followed by no less than three pretenders. Huhanye managed to keep his throne by submitting to the Han, but could not subdue his elder bother Zhizhi Chanyu who had allied with the Kangju and set up a rival kingdom in Turkestan.
The Raven had sided with Zhizhi and shared his fate when he was finaly defeated by the Han in 36 BC. They fled west and disapeared from history, for a time.
A few individuals took refuge in the Chinese army then became herders or farmers. They had no immediate impact upon the history of either Xiong-Nu or Han, but their sinicized descendants would.