L.L.
I'd say who cares about around the ice maker...as long as it's clean, I'd feel okay about it. After all, it isn't open to the public eye. :)
The handles, however...I have the same issue with the same fridge. I use comet. I use comet for everything, and it seems to work for everything. Rub it in good with a rag and let it set for 15-20 minutes, then rinse. Repeat. :)