Short-billed Dowitcher has not been recorded in Hong Kong. It is very similar to Long-billed, and very difficult to separate (incidentally, bill length is not the best way to separate them because they ovelap). Short-billed breeds only in North America and is therefore perhaps less likely than Long-billed, which mostly winters in America but breeds in both America and Asia.
In fact, I think think most records of small dowitchers in Hong Kong (i.e. not including Asian Dowitcher) do not look closely to consider the possibility of Short-billed. Those that have considered the possibility have confirmed that the bird involved was Long-billed.
Short-billed is a potential vagrant to Hong Kong (Lesser Yellowlegs is another American species that has been seen here) so it still may be worth paying close attention to these dowitchers.