I just showed your views to two random female colleagues and the feedback I got included the words "old-fashioned", "out of touch", "are women considered less worthy and weaker", and last but not least "sexist", but they appreciated that you had good intentions.
On their possible responses, they would not tell you off for it, but if faced with that offer, they would both decline with a very disapproving "but thank you anyway".
Personally I would offer a seat to a woman breastfeeding if stood up, as they do have a genuine need for it, but not simply because someone is female, just to clarify.