Most of the shows (like Beauty and the Beast, Indiana Jones Stunt Show) are performed in covered auditoriums, so they will be no problem during the show.
One I can think of that is not is Lights, Motor, Action. Most of the wait in line is covered, but the show itself is presented in an open theater, totally in the sun during the show.
There is a GAC for sun sensitivity, and I feel I can say this on this board bc it is a rather useless GAC, as well as a hard one to get in that not everyone had the stamp for it. CMs must not see it a lot. I do not do well in direct sun (meds) and get sun poisoning very easily so here are some thoughts.
It's kind of a 'nebulous' stamp. I don't remember the exact wording, but when I saw it last it was something like
Wait in a place out of the sun when the queue is in the sun for a considerable period of time.
Kind of up for a lot of different interpretations.
(2) Haunted Mansion. Hard one, request to NOT wait by the hearse and be allowed to wait under the canopy. I have big issues with this, they send you by the exit which is no better than the hearse and I have to ask for help again and it lands me outside for more than I care for;
For people using wheelchairs,
ECVs or strollers as wheelchairs, you have to wait at the hearse (which is in the sun) in order to get to the accessible boarding area.
For people without those, you will be waiting in the regular line, which does have a roof over pretty much the entire line. Depending on the sun angle, the entire queue may not be shaded, but by moving around members of your party you should be able to keep the child pretty well shaded.
(3) Nemo show. They will tell you to come back but mistake, it puts you in the regular line and you end up getting a lot of exposure, ask to be able to return at the front. I got sun poisoning on this one, be careful of the line.
Nemo at AK is a bad one because there is little shade in the queue. We managed it by having DD's back to the sun and having taller members of our family shade her. This doesn't work around noon when the sun is close to directly overhead, but is quite manageable at other times of day.
Once you have gotten in, the theater is actually inside.
(4) special events, ask CMs and explain your situation (GAC will likely not help).
The GAC is primarily for attractions. In other situations, the CM might be able to work something out, but they often have few accommodations available they can offer at non-attractions.
Some other things to think about (many were already mentioned by other posters):
Go as early as possible in the morning. Doing that misses the strongest sun and also makes more shadows to move in. Lines are also shorter early in the morning; even during Spring break, it's possible to go on all the Fantasyland attractions by 10:30am, some several times.