Hey James,
For a patient-perspective, I separated my shoulder about 15 years ago and had bi-weekly to monthly separations afterwards. In discussing with my surgeon, I went without surgery. There are distinct ranges of motion I avoid (climbing overhangs where I am required to reach above and behind my head) and with that I have been able to go 5 years without separation and no real impact on my activity level; I am still able to climb as hard as I want and don’t think there would be an issue swinging tools in vertical ice (though I don’t ice climb).
Obviously your results may vary depending on the details of your injury and you should listen to your doctor but thought I would share in case it is helpful.
Good luck on your recovery!