I hope somebody can still benefit from my answer, but either way I am giving my two cents
The stinging problem really depends on a lot of factors for example what kind of water your kid swims in or how fast she gets used to it. Salt water is always great for people with ichthyose, but it is also the water that stings the most. When I was a child, my mum needed to force me to take my salt bath because I was so afraid of the water hurting my open wounds. Even as a healthy person you might know what I'm talking about if you'ver ever swom in the ocean with an open wound.
I can second stc's opinion about clorinated water, it doesn't sting, but you should always shower your kid thoroughly afterwards because it makes the skin dry and itchy.
The second factor is scratching. If you skin feels itchy, you wil scratch it, but if you have ichthyose this itch might very well turn bloody because you scratch too much. Especially kids have problems dealing with that. It's like having the chickenpocks. You know you shouldn't scratch yourself, but you still can't help it. Those scratchmarks are often the ones that hurt the most in the water.
As a basic rule, if your kid feels that the water is unbearable, you will notice it. My mum told me that I was vocal enough about it even when I couldn't speak. After some time she knew exactly when I really couldn't take it and when I was just throwing a tantrum. Just start with a small body part, like an arm or a leg, to test the water so to speak
In general, I can only stress: Water is GREAT!!!! I absolutly love taking baths, swiming ot showering. My skin doesn't feel dry in water and when I was a kid, the water was also the only place where I truly felt in my element. My skin felt normal and didn't really look all that different from the other kids (especially under water). It's also a good form of sport (as already mentioned) because sweating and clothes are not really an issue. So try to let your kid get used to water as early as possible.