Cheer competitions next year will start Wednesday the 22nd of April and go basically through May 10. The competitions on May 1-3 and May 8-10 will be the largest. If you do a search you will see a really wide range of experiences with the cheerleaders. In general, the people who think it's the most awful are those who've been at the resorts where they are. The impact on the parks is minimal. One of the competitions next year is at the Contemporary because there's a sports thing going on at WWoS (I'd have to look up which one it is and the dates), and I think that will have a bigger impact because of the proximity to MK. The resorts impacted will mostly be the All Stars, Pop, and CS. Some years some of them have been at CBR as well and some of the other moderates. The best advice for avoiding them seems to be to stay deluxe (bot not at Contemporary next year during the one that's there...)
We went this year the week after the cheer competitions ended. Crowds were lovely but it was hot already. I would go again that week though, for sure. It only rained once the entire time we were there. From your dates I would choose April 25-May 2 if you want it to be maybe slightly cooler and can deal with the cheerleaders, or May 16-23 if you can tolerate the warmer temps.