i dont have arthritis but i do have shoulder pains as well...i think using a weight that is comfortable and doesnt cause much pain would do fine.
lifting heavy will only cause more pains and issue and can do some damage.
i use to lift heavy and i would do good for a short period of time and then hurt myself again so now i use a comfortable weight and press it as many times as i can. my ego might hurt a bit but im able to go back to gym and do more workouts.
I'd listen to my body if I was you. If a certain exercise bothers your shoulders find an alternative, but keep whatever program is getting you results.