Few good recommendations made already. New (decent) cables, properly greased/lubed, will make a difference and is the cheapest option.
As njee20 says, gripshift is perhaps a good option. Assuming that your arthritis is only a problem whilst pushing something with your thumb that is, and you can still maintain a good gripping action between your thumb and forefinger, whilst twisting your wrist to shift…
Or go for some new Shimano (SLX or above IMO) trigger shifters. Personally I find the Shimano shifters have a much lighter action, particularly on the thumb lever, than SRAM shifters do. And the latest generation SLX, XT and XTR shifters seem a step up over anything previous from Shimano too. Fitted a set of SLX shifters to one of my bikes, and couldn't believe how light the shift action was compared to older LX and XT shifters even.
Or as has been said, you could go for an Alfine rear hub, which puts the single shifter on the right hand side of the bars. If you've got loads of cash to spare, you could even go for a Rohloff!