to indicate a character's tone of voice.
to indicate a character’s tone of voice
The stage directions are found inside of the parentheses "(with the gallantry of a young politician)". The use of the preposition "with" tells us that the following lines should be said as if the character has "the gallantry of a young politician". This means that there should be some arrogance and courage behind his question. In a way he's saving the women, but also acknowledging their troublesome traits..
Given that he is referring to the ladies, he has to change the tone of his voice a bit to appeal to them more. He cannot speak in a manly voice which he would normally use while speaking to other men, but rather appear more suave and gentleman-like.