WARNING this is based on actual experience not speculation or hearsay. You have been warned.

So just an update on this. Congrats, I did some legwork for you.
First of all, presenting male or androgynous is an extremely bad idea if you look female. I did (t shirt and jeans) and it did nothing but confuse Korean airport security who kept bouncing me from line to line. First they directed me to the women's then after a few minutes the security guard yanked me to the men's after talking to the guy checking passports. Then I showed my driver license which was updated and they put me back in the women's line. Then when I got there the screener looked at my passport, looked at me then called over a man to wand me down. They have male and female security lines.
I couldn't talk and they confiscated my phone so I couldn't type!
Btw I was asked by everyone who saw my passport if it was really me. Even the woman in the casino checking passports before you can gamble. (Only foreigners are allowed to gamble and they check your passport). I wrote down "I am transgender and that is an old picture when I was a man" and she gave me a kind of a grin. I didn't really want to have to out myself to everyone.
I filed a complaint and they promised they would educate the airport security so your experience on the return may be better but YMMV.
My advice? Present how you damn well please and be prepared to explain to Korean authorities anyway because you may have to anyway. Preferably on paper in Korean.
In the USA on return I had absolutely NO problems. The TSA on my way out of New York gave me NO issues except setting off the scanner (due to my donor material in my pants) and I just said, "I'm trans" and that set off a lightbulb in their heads.
If your passport has an old pic you're going to be treated with scrutiny anyway.