I don’t think it really matters if your shirt is wrinkled*. I used to work a suit and tie job in a past life, while the suit part would get regularly dry cleaned, the inner button down shirt and slacks would get washed and dried with the rest of the laundry and never ironed. Nobody ever said, emailed, sticky noted a damn thing that affected my career or social work-life sooo ¯_(ツ)_/¯
*Except the following groups: Politicians, Celebrities, Rich people, Executives.