Yeah, I'd recommend giving her something for her hands. A small blanket, toy, nursing necklace, your finger to hold, baby's ear, etc. I also tend to pin one arm as much as I can between their body and mine, but that depends on your positioning, but one less wandering hand is good. But yeah, I don't mind gentle touches, but I just redirect all of it because being pinched, poked, punched, scratched, etc. is not tolerable for me, so it is not allowed. At my babies' age, they don't understand yet, but can be redirected. I usually just give them each a spit rag (small size cloth diapers) and that keeps their hands busy.
And as far as cutting nails go, yeah baby nails are sharp no matter how short they are in my experience, so you aren't doing it wrong