i used to play acoustic guitar, and when i tried a couple guitars with tighter string spacing, not only did my fretting hand cramp, hurt and swell - sometimes my fingers would stop working. my wrist hurt, too, and after playing it started hurting for longer and longer. so i made sure to play guitars with wider nuts, and i never had issues with them unless playing a sharper V neck, which i stopped playing.
some bass necks make my hand cramp and hurt, some don't. mostly the basses that gave me issues had wider necks or very thick necks, so i stopped playing them, the issues went away, and so i sold the basses with the necks that caused me discomfort. issue gone. i do find the bass vi uncomfortable as the strings are so tightly packed together, which is why i never bought one.
that being said, even before i developed arthritis, i needed to lower my string gauge on bass and use more flexible strings, which also helped any issues i had been having and allowed me to increase my playing time from an hour or two to four to six hours without pain. i still use extra light strings to this day. they helped me a lot, especially after arthritis. and it took some experimenting to find which strings were more comfortable.
but if you can't quickly and easily fix the issue by changing basses or strings, a specialist is probably the way to go. you don't want to risk your hand mobility!
Play the bass that doesn't hurt.
From what you've said it seems simple: a functional use issue caused by the relationship of your body to that bass.
I mean you could do detective work and identify the exact problem, but man, just play the ones that don't hurt.
i wish i could like this more than once - it pretty much sums everything i said up. play the basses that don't hurt.