I suppose there is no fast train from Beijing airport to Handan East Station directly, so please suggest what is best way ? I do not intend staying in the city

You are right that no direct fast train is in operation from the airport to Handan. Upon landing, take airport shuttle bus line 7 to local West Train Station. There you can take a bulle train to Handan East.

From Handan to HK, you can fly to Shanghai (Pudong Airport is best) first and then transfer to another flight to Hk.