Ooooh, cc - it's my Jersey, not a goat, that I milk but I absolutely understand how you feel. My hands ache arthritically sometimes and I know it is only a matter of time before I can no longer do this by hand. I'll keep going while it's physically possible because that 10-15 minutes in the morning is my favourite part of the day. Just me and my girl, rhythmic swoosh swoosh into the bucket, she providing and me too, head on flank, reading each other and communicating in a way that only we two understand... priceless.
CC, jaykay will be along soon to remind us all about the device she uses to milk her goats - it's the nearest thing to handmilking without using your hands, and it's one of the things I will look into when eventually the pain and lack of mobility in my knuckles get the better of me.
Meanwhile, I presume there isn't some kind of elasticated glovey thing you could wear to keep your joints in their place?