There is no directive of the Sharī‘ah which explicitly prohibits a Muslim
to shake hands with a woman who is not his mahram; therefore, it cannot
be regarded as a Sunnah of the Prophet (sws); however, shaking hands with
a woman is something which was personally disliked by the Prophet (sws) as is
mentioned in certain Ahādith (as you have also referred to). I think
Muslims should refrain from acts disliked by their Prophet (sws). Of course,
They have not been bound by Islam in this regard.
The question may arise about the
status of the personal likes and dislikes of the Prophet (sws) as regards their
validity for his followers. In this regard, I think two distinct categories can
i. A like or dislike which has some
ii. A like or a dislike which has
no moral basis.
Since Muslims are required to
follow the moral example set by the Prophet (sws), the first category of likes
and dislikes should be followed by them as much as they are able to in order to
reap high rewards in the Hereafter. This of course does not apply to the second
category, examples of which include the Prophet’s like for certain colours or
his dislike for certain type of foods.
Shaking hands with a woman is a
dislike that belongs to the first category, and, therefore, a moral standard
that is highly desirable to be followed.