If you Google "US Navy 1925 hat image", or replace the year with WWI or WWII you will get an idea of what the US caps looked like. All look familiar to me, raised in the US, and do not look like the hat in your picture of Joseph Audley.
I associate the style of his hat with some other country, but I just can't place which. If you can rule out the UK,then maybe it was Canada or Australia, I don't know.
Someone on this board will know for sure, the answers to UK military questions that I read here amaze me.