I don't doubt that Weird Al made handwritten notes.

Although portable typewriters were definitely a thing in 1985, they were loud. (Libraries were still a shhhhh zone back then.) Plus people didn't really take notes on a typewriter. Typewriters were generally used once you had all your notes and were ready to type your final document (or at least a first draft).

Photocopiers were definitely available in Southern California libraries (where Weird Al grew most likely resides). I know that my library had one in 1967. However, they were fairly expensive to use.

Besides, given the lyrics, I don't think he was taking down massive amounts of duck details.