well, jent (and all the others) has the appropriate response for this bochur’s behavior:; It is a Mitzvos assay” to rise before an older person.(Mipnei seivah tokum)It is no even a question whether to give one’ seat up because maybe, maybe you would be touching another gender by accident.
As far as shaking hands with another gender, (to noitallmr and jent), first of all, this may not even be a problem for a woman.She may not be under the issur of “loi sikroivu”. second ,even for a man, touching which is not for ‘chibah” (closeness and sensuality) is not ossur. This is clear from a number of sugyos in shas. (Quotes at your request).
In Germany and Hungary, it was the custom to shake hands as politeness and good jews (even rabbonim) did it all the time. So, very respectfully, it is not an “issur” to shake hands, regardless of what you may think. It may very well be midas chassidus and ,jent, if you want to you are welcome to do this, but don’t denigrate people who do shake hands.
there is an Igros Moshe on this and various gemoros.