We did DL, not WDW, with our daughter who was just a bit younger than your 3 year old. She did great on POTC and it ended up being one of her favorite rides- she's really familiar with Peter Pan and had even chosen to be Captain Hook for Halloween, so the pirate theme was not at all scary to her. I had told her in advance that the ride would be dark, and I warned her about the cannonball scene. We turned it into a funny joke about them trying to throw things at each other so that when we went through it she just laughed and thought it was great. I think it helped her knowing that she was not the target. And she knew the song, which added to the fun.
The Tiki birds were another big hit-- again- we had learned the song well in advance, which helped. But being in DL, that was the original version, not the new one. Same goes for HM which was done up for Christmas at the time. I'm not sure she would have liked it otherwise.
Anything with thunder/lightning was not a problem as we go occasionally to the Tempe Rainforest Cafe and she the "storms" are her favorite part of the meal. :shrug: Disney just does it better!
ETA- we had also made up this whole thing before we went that bad guys sometimes went to the parks too (Jafar, Maleficent, Captain Hook, etc) but that even though they were still a little grumpy, they always, ALWAYS behaved in the parks, because Mickey won't allow them in otherwise and the threat of being banned was enough to keep them in line. So whoever she saw walking around, or in the rides-- the witch in Snow White's Scary Adventures, for example-- she felt completely safe. I know she kept it in her mind because she brought it up several times for reassurance :lol: