Edit: fixed the attachments.
Smashed out another mallet tonight. The hole in the green wood was a pain to make, but I finally got there by chiseling enough of a hole to then use a drill bit/auger.
Took a fair bit of whittling the handle and trying it in the hole, only to get it stuck halfway and then bash it back out with a metal rod to whittle down some more.
I peeled the bark off the hammer part, but I left the bark on the handle for now. I will probably shape the handle a bit more in the future.
Here are the photos: