I Ave severe arthritis in my right thumb.  Some days a BC reel is out of the question.  I fish mostly stained to muddy water.  What finesse baits do you recommend?  Or, would you just fish with a stiff spinning rod with what I would use on a BC? (I.e., t rig, jig, spinner,etc)

Sorry to hear about your ailment. I'm just starting to feel it on some hand joints. You can fish most lures on spinning that you do with BCs. Just match the action/power of the rod to the lures. There certainly aren't as many spinning rods on the racks as BCs for standard or larger bass lures, but they are made. Also rods meant for other fishing often make perfectly good bass rods. 

As far as finesse baits, small jigs, JBs and cranks, t-rigs, and swim jigs can all be used with spinning. Don't throw a 3/16 Baby Boo with a flat Abert unless you want your thumb to really hurt...