We have had shower issues here and I have to say that I am SO relieved to hear I am not the only one!!
Our bathroom set up is odd, we have an ensuite which has a shower, and it is directly above LO's bedroom. For ages he was in our bedroom and I used to shower at night when he was sleeping and it never once woke him up. Then once we moved him into his own room, I got paranoid that the shower above him would wake him up, although it never woke him when he was next to it! The water draining is louder when you are underneath, though.
BUT I agree with PPs that your LO will have to learn to sleep through the shower, and trust me, he will! Esp if you have white noise going, it's not likely he will wake. We also hold off on flushing until he's awake, for naps only, I've learned that at night time, he's OUT and won't wake, so the shower probably won't either.
Truthfully, it wasn't until the past month or so that I started showering during the day when I am home alone with DS. Most of the winter I got showers on weekends only it seemed. It made me SO crabby and grouchy, I used to blame it on DH and we fought constantly. All I needed was 20 minutes to feel human again and when I got it, I think he realised his life was easier for not having to put up with me!
We didn't have a chair that I could carry up the stairs and fit into the bathroom and close the door as the ensuite is very tiny - shower, toilet, sink, no space. But, one day DH suggested the carseat. I started taking the carseat up, putting it in front of the shower and strapping DS in. Gave him a dummy, a lovey and some toys and got in. If he fussed I opened the door, handed him a new toy, a little tickle and he was happy again.
Now that he is older, and not happy to do that, we have a next stage car seat, a proper "sit up" one. We don't use it in the car because it's not rear-facing, but he's more than comfortable being strapped in it. It sits permanently in our bedroom facing the TV, and I put a Teletubbies DVD on, give him lovey, dummy and the DVD box and go shower. He shouts at me when the parts he doesn't like come on and I have to run out and hit the skip button and run back in. I can't say I ENJOY my showers as they are as fast as possible, not relaxing and I'm COLD because I have to leave the shower door open so that I can hear him. But I do get clean!!!!