I had the same surgery on my right shoulder and I'm right handed. I did fine with shaving, brushing my teeth, et al. As a matter of fact, I went on a fishing vacation in the Pisgah Forest with my son and a great buddy. We were skipping stones in the river and I was no longer in a sling, but still going through PT. I was still slowly beginning to use my right arm again, but NOT for throwing. I was using my left arm and I skipped a rock further than both my son or my buddy. They were floored at how well I could throw lefty.
That was 2008 and I have no regrets and full mobility. Very successful for me, I wish you luck! Just keep up the PT.
Oh yeah, PT just might hurt a little.
Who am I kidding, the first time I tried to raise my arm as instructed, I nearly passed out. And when I didn't, I nearly vomited. Good times.
Notice the smiley using his left arm?