It sounds rather neurological. As though something is affecting sensory nerve function - though why it should be OK when you are on dialysis and only occur off dialysis is odd ... unless you sleep in a different position (neck/shoulder especially) when NOT on dialysis. To me, this has all the hallmarks of a positional issue with your cervical spine and neck!
I am guessing, now, but are you sleeping in a more structured position when you ARE on dialysis (eg: propped up on pillows with your dialysis fistula arm also supported by a pillow) but then, on the nights you are NOT on dialysis, you are more snuggled down on your side?
If so, this suggests a positional problem with your cervical spine ... perhaps Cx discs 4-5-6-7 with the 5-6 disc predominating. Having had a compressed fracture of my 5th cervical vertebra as a 21 year old, I have similar symptoms myself. It is annoying, but not life-threatening!
I may be right off the mark here (though I suspect not) but it doesn't sound dialysis-related to me ... and certainly not something with the fistula ... but something more positional/skeletal/disc/nerve-root compression related.
If you ARE sleeping differently off dialysis compared to on dialysis, try mimicing your dialysis position when sleeping on your non-dialysis nights ... and see if that works. Then, at least, you'll know you have an annoying problem, but one that wont kill you.