I know you want to honour your nan and that's fair enough and in fact lovely, but you need to be fair on your child as well, and no I don't think Cooper is appropriate as a first name for a girl so it would fail as being fair on her IMHO.
Some parents like so called strong masculine names on daughters, and, if you do, Cooper fits that ticket okay - but, with the meaning of a beer barrel maker, and so commonplace a surname, I wouldn't be impressed with it for a boy, and as for a girl - how many girls really want to have and to go through life with a distinctly masculine name? I don't think many do, or at least, many don't. One of my friends is called Samantha, and she was always called Sam growing up - and she even hated that, and from early adulthood insisted on people calling her Manth or Manthie for short instead.
Cooper is okay for a middle name. But in your shoes I would look at using a variant of your nan's name instead, a feminine sounding one.
Okay so many of your relatives have already used your nan's name for their daughters but most names have variants. For example, I'm thinking of giving my daughter the middle name Pearl to honour my great grandmother, whose name was Margaret. I don't like the name Margaret - too harsh a sound for me - but it means Pearl, and Margaret means Pearl, so for me that's after my great grandmother.