What Causes Weakness And Tremors In The Right Hand?
A peripheral nervous system condition suspected.
Detailed Answer:
I read your question carefully and I understand your concern.
If you are certain that there is no accompanying weakness of the lower limb and face on the right, then a brain issue is unlikely (usually there is weakness involving the whole half of the body and face). It would be more likely in the setting of an issue of the peripheral nervous system.
The most common peripheral cause of hand weakness is a peripheral nerve compression. Carpal tunnel syndrome is one possibility, compression of the median nerve in the wrist. It is more common in people suffering from arthritis since you mention it (but can happen without a history of arthritis).
Another common nerve compression site would be of the nerve root or spinal cord in the neck, also common with a history of arthritis.
Among other possibilities to look into motor neuron disease would be something else to consider.
So it needs some looking into. I would start with a neurological physical exam from your primary physician or a neurologist, to search for other neurological signs such as muscle wasting, alteration of the reflexes, sensory changes etc. Most probably some tests will also be needed in particular nerve conduction studies with electromyography, when neck compression is suspected by findings a neck MRI as well.
I remain at your disposal for other questions.