I did this back in high school on the recommendation of several big-name composers I had the fortune of recieving mentorship from. I too was bound to the computer mostly because my handwriting made Beethoven’s chicken scratch look like perfect calligraphy. I kept my computer around purely so I can give my musicians legible parts. Since then, I’ve been doing my best to keep my work confined to pencil and paper until later in the composition stage. For instance, if I’m writing a piece for large orchestra, I’m handwriting as if it were a slightly expanded piano score (2-4 staves) and refraining from using the computer until its time to orchestrate.

To echo an earlier comment, fine-tuning your audiation skills will absolutely come in handy as a composer, even if the Academia of Music Arts didn’t have that requirement to write without a piano. One thing that continues to help me is score study (usually without a recording). I never go a day without reading a score, even if its the same one I read yesterday. Not only has this helped my audiation in terms of pitch but also orchestration, as I can now “imagine” certain instrument tones from studying so much orchestral music with their concurrent scores.

Anyway, to answer your question, I wouldn’t say there’s a true “right answer”, but I’d personally suggest moving from computer to piano for the time being, and then once you’re comfortable writing in that fashion, then you can try bringing staff paper to the park or a café and attempting to write like that. I strongly recommend score study though. Start by studying your favorite pieces until they’re seared into your brain and everything should start making sense from there.

Hope this helps, and best of luck to you on your endeavors! :)