Most speeches do not have to be fully written
out and need only minimal memorization.
Speeches usually do not have to be fully written out, and only the opening and close have to be memorized.
Improvising as speaker is similar to improv with a partner, but limited prep doesn't mean just winging it.
Soaring with either is mind-blowing.
My first speech in a college class was read off my eyelids: that was an assessment by a classmate, and she was right. It was memorized and seemed more mechanical than natural conversation.
Even after years as a veteran Toastmaster, I still didn't always succeed in making a memorized speech seem unmemorized and natural.
That all changed when I was forced to change my technique. Another member of my Toastmaster club canceled the evening before he was to speak. I took up the challenge to fill his spot on the subject of "Being Politically Incorrect." In three hours I had my speech ready. The key was choosing a topic I had anecdotes from my past to tell, focusing on a theme my stories and one point of research could support, creating a catchy opening and clincher, and then practicing aloud. A speech that is more improvised than memorized may work for you.
This speech was another sort of improvised speech, this time reporting on jury duty that was to start the very next week. The recording goes four minutes before the battery died. Still, you can get the idea of the overall flow with the speaker having little prep time.