April is a little early in terms of weather but you may be fine. It will still be hot ad humid and maybe some rain.
No you dont need a guide. You will be safe from crocs if you stay where you should on paths and do not swim anywhere you are advised not to.
Go to the Bowali Visitors centre and see what is open and what is not, and the lovely people there will tell you what to stay away from.
https://northernterritory.com/kakadu-and-surrounds/see-and-do/bowali-visitor-centre
Itis better to swim in Litchfield in places that are open for swimming. You may find in Kakadu that the gravel roads will still be shut so you will not get to waterfalls like Gunlom and Jim Jim, but you just have to wait and see.
I also suggest that you take a cooler bag and have some ice bricks and have your kids snacks, water and fruit, as there are few options for shops out there. You will not find cafes and shops and all that!!