Thanks everyone for suggestions! I quite like May/Mae and Micky, I might run them by my friends to see if they work. Moira, Ree and Minnie are interesting - not sure if they'd suit me but I'm definitely intrigued by them! Molly, although I love, is a no-go for me as one of my best friends is a Mary nicknamed Molly. I also like Polly, but I know a Polly who's... very interesting, and to me, I would always associate that name with her.
My middle name is Noreen, but I really dislike it and have wanted to change it. However it honours my grandmother, so I've been thinking of changing it to Nora, so my grandmother is still honoured and I have a name that I like a bit better. Would there be any nicknames that could incorporate this?
Thank you all so far, you've been a great help!