There is much debate here in the US about the shaking of a woman's hand, let alone giving her a hug. People debate about the hadīth in which the Prophet expressed his personal dislike on shaking hands with women. Some say this was his own personal thing, others say it is Sunnah so it is for everyone. I would like to know your views.
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 be identified:
i. A like or dislike which has some moral basis.
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.