If you go ahead with the operation, get the Shoulderdoc Shoulder Exercise Book. The exercises in it are far more effective than the ones given by physiotherapists. They are classified by type (range of movement, proprioceptive, strengthening, core stability) and intensity level (1–3). It’s small and comb-bound so that you can fold it flat and easily see it while exercising. … Oh dear, I just checked and found that the 2008 printed edition of the book no longer exists but you can get free access to an online version on shoulderdoc.co.uk.
Attend physiotherapy anyway because, if you don’t get the range of motion you expect, they can refer you to hydrotherapy, which is amazingly good for shoulder rehab. The NHS typically gives you only a few sessions. But once you have learned how to do exercises in the pool from a hydrotherapist, you can try to find a private hot pool and continue do the exercises on your own (if there is such a pool near you and if you can afford it).
Also, get a shoulder pulley and find videos showing exercises to do with it.
People get shoulder replacements for two reasons: for pain or for trauma. People who have pain, like you, are more pleased with the outcome than trauma patients because they are so relieved not to be in pain any more. People who have had an accident are less pleased because one day they have normal strength and range of motion and the next day they are severely limited and the operation does not restore perfect function. This means that trauma patients are quite motivated to do the exercises, whereas some pain patients don’t push themselves to do all the exercises because they figure that the level of recovery they have achieved is good enough. But if you accept significantly reduced motion/strength post-op, you may have problems later on; you may be more prone to falls and less likely to be able to get up if you do fall; you may no longer be able to reach things on a high shelf; you may not be able to do an action requiring you to twist your arm around something; you may not be able to carry your shopping home. So I hope you can find the motivation to do the post-op rehab exercises every day until you reach a plateau – and then continue in case that’s just a temporary levelling off of progress!
Good luck.