I doubt you will have a problem with it. I have short fat fingers. I am much more comfortable with a P neck than a J. But, it may be because I started with a P. I own 2 Js, but I have always found the J neck to be claustrophobic.Thanks i have big hands but your right i should play a few .
My goto is a MIM P. Just got it back from the shop last night. I put Labella 760Ms on it and had to have the nut slots filed and a setup done. Lovin' me some fat flats.