You can put Penguin's cigar in his mouth. It's a very taxing thing to do and it takes patience.
What I do is I tuck it in the right corner of his mouth then SLOWLY rotate it around until the cigar hits a sweet spot where it's wedged in his mouth. It takes a lot of patience and attempts. And it is a fragile connection. Pose him, particularly his head, before putting the cigar in. I could make a video to try and help if anyone would like.
I don't normally display him with the hat, I just didn't want to lose it while moving my Arkham figures to a new shelf.