IMHO age is not the vital issue here, although the park has to put some type of limit in order to warn parents that there are requirements that need to be met.
It is the childs confidence and ability in water that counts. I have no doubt my elder daughter would have managed fine at age 4 with the swim, she spent a lot of time in the water and was a confident swimmer at that age, my youngest is now 12 and I'm still not certain she would enjoy the swim. She can swim well enough but hates being in water more than 6 feet deep, which makes no sense because shes less than 5 feet and can drown just as easily in 6 feet as she could in 10 !!!. You as a parent know them better than anyone. DC is a great experience and one they should treasure for many years, if they are scared or not ready to do the swim it won't be nice for them and you'll feel you wasted a lot of money. IMHO if you have any doubt AND you know you'll make a repeat trip in a year or two, I'd put it off until you're certain they will really enjoy the day there ( and you feel it's money well spent). It's a tough call because kids can change on a day to day basis sometimes LOL.