Of course you (or anyone) don 't need to have surgery to conform to other people’s gender stereotypes. But I don’t think that’s what was implied here.
What’s “feminine”? is that not a gender stereotype? I don’t think there’s anything wrong about being a man that closer fits a feminine stereotype than a masculine one.
What I said is that for a trans, “gender relates to what stereotype (social construct) a person identifies with”. I did not say their gender matches a particular stereotype, but that it relates to it.
Someone who does not identify with a typical stereotype and believes that this makes them be of a different gender, is defining their gender based on whether they fit (or don’t fit, in this case) a specific social stereotype.
However, someone who does not believe gender relates to stereotypes at all would not see that person as having a different gender because that person’s gender (for those people) would be unrelated to whether they match (or identify themselves with) a stereotype or not.