The splint is there to limit movement in the finger, from what i am interpreting. I would still have them doing arm/shoulder exercises. Probably should modify what you use for resistance. How you modify would depend on which finger. Strength tubing between other fingers, as long as its not causing pain, would work.
But I would still exercise upper body. If hand/wrist is in a full splint or cast that might be different. I wouldnt give up the whole arm for one finger.