Lots of cool suggestions but most of them aren't anywhere near a jazz or P/J.
The P/J mustang is probably the best suggestion so far IMO and I can't think of anything better that's P/J + shortscale.
If P/J isn't an absolute necessity I would look for a used 60s Hagstrom HB II in good condition. I often see them on ebay at reasonable prices. They are lighter than most hollowbodies, very thin body, extremely slim short scale neck, very comfortable and easy on both hands, responds really well to a light touch, no need to dig in hard for a powerful tone. I honestly can't think of a better bass for someone with artrithis. But it doesn't sound like a J. More in the direction of a P-sound, fat but sits nicely in the mix.
The only downside is that they are starting to get a bit old by now and the switches have a tendency to crap out. But the neck is impressively stable. Hagstrom used a very unique truss rod system at the time and it seems to be working great. I've owned one of these basses for around 20 years and I've never even once had to adjust the truss rod. I've got flats on mine and that insanely slim neck hasn't moved at all over all these years. I have the action set REALLY low with no buzz anywhere. Great craftmanship in these old Swedish Hagstroms.
They originally came with a non-adjustable wooden bridge so intonation may be an issue but the currently available Guild Starfire Bridge is more or less a drop in replacement that fixes this.
I read somewhere that this was the bass Jimi Hendrix used in the studio. Makes sense because it's so easy on the hands that someone used to guitar should be able to instantly adapt.