Hi, Toby has been the same since he was born and he's now nearly 7 months! When he was little swaddling worked best. Scratch mitts are useless, the sleepsuits with integral scratchmitts are fab though (I like the Next ones best but lots of places sell them). Unfortunately most only do the integral scratchmitts up to 6 months and my big boy has way outgrown those so we are back to lots of scratches every day

We are no longer swaddling so he only option left for us is socks on his hands!! He just pulls them off with his mouth though.
I keep his nails super short but it doesn't really matter how short they are, if they scratch hard enough they will break the skin.
Sorry not much help but as your LO is still little thought I would recommend swaddling and sleepsuits with mitts.
C