No, adding anything to the storage on your phone will not slow it down in any way.
I've got 20.7GB of music, 16.7GB of Videos, and 4.8 GB of photos, 2 Gb of books, 1.9GB of Messages, among other things on my iPhone 6 Plus 128GB. It's as fast as it was when it was empty.
There's 128GB of storage on your phone. It's meant to be used. 🙂 And 10GB will barely put a dent in that available space.