What is the ruling on shaking hands with or kissing a woman who is not a mahram to me, and am I sinful if I shake hands with my female cousins (paternal or maternal) reluctantly to avoid embarrassment?

If the woman is a non-mahram, it is not permissible for her to touch or kiss you, and it makes no difference whether she is a friend of your mother or treats you as her son. Paternal and maternal cousins are non-mahrams; it is not permissible to shake their hands. They must be enjoined to good and forbidden from evil with wisdom. It is not permissible to shake their hands out of shyness towards them, for Allah is more deserving of sh shyness. Customs that contradict the Sharia must be changed.