Perhaps I should have mentioned earlier... I've got hands like a pound of pork sausages, but it hasn't stopped me playing fairly narrow necked instruments - including the mandolin and banjo.
I play fairly complicated Ragtime guitar, so I'm not just a chord basher. Mind over matter, y'see... it's got a lot to do with disciplining your fingers to fret correctly - fat fingers aren't necessarily a problem. Not for me, anyway!