I ask this question because support and reassurance, by shaking a hand and patting a crying patient on the back, are professionally regarded as an appropriate means by which to relieve his/her anxiety. Is it in order to shake the hands of a non-mahram patient if she presents her hand for shaking either prior to commencing treatment – where contact is unavoidable, or after having completed the treatment?

In as much as that is totally professional behaviour, there is no harm in it.