The suggestion of using a balloon is a good idea.
With my husband I used a soft medium sized ball with general questions on it (available from the Alzheimer's Society shop). It helped start up conversations, got us laughing and reminiscing - as well as helping him exercise by gently throwing and catching.
Just by chance, there was one time when he picked up a stretchy resistance band belonging to our daughter. She used it to tone up her legs but my husband liked to stretch it with his hands /arms. I believe you can get them with different levels of resistance.
He also liked to shake a tambourine or maracas to the beat of the different kinds of music we listened to.
If there was football on tv I would give him his football scarf and often he would hold it above his head and sway his arms in support of his team.
He was actually fairly mobile until late on into his illness, but on days when he struggled and preferred to sit, we used to have fun with an exercise based on the children's song 'Head, Shoulders, Knees and Toes '. We did the routine sitting in a chair and mainly he would copy me. It didn't matter if he got it wrong at times, the main thing was that he was moving and enjoying it.
Edit:Just to add that I just remembered that on the secure dementia ward my husband attended during his final months, the staff often brought out a lovely colourful beach ball for the patients to pass or throw around. My husband didn't involve himself in that - but it was very popular with others.