In short, not UK()LeLee but FISH MOUNTAIN LEE ~ with some sort of stand in at the \ which I think might be a Chinese way of rendering MAN or PERSON.
Any of you folks take shorthand? I didn't but I lived with a professional steno for many years (my mother), and she could take dictation faster than folks could talk. The Chinese invented something like stenography in this flowing script method.
I'd like someone who knows either or both of the two major steno systems in America to look at that "signature" and tell us what it says. What I have here looks like "Hawaii" (fish mountain) person "Lee".
You can find many thousands of Chinese characters and script representations on the internet, so I didn't come with this out of my imagination. I went looking for the characters and they were there. Steno is different.
I’ve never heard of or seen any official signatures on state documents using shorthand, stenography or Chinese characters. If any documents can be found from HI using anything like that then maybe your theory might be useful.