Looks simple enough. My dad’s old 2002 Huskee lawnmower uses this same rear axle setup. The axle on his old lawnmower broke and needs to be replaced. He just hasn’t gotten around to it for a some years now.
If it does that on carpet... its going to zip in the water. Looks like it's weight is balanced well, too. Get some board wax for the bottom of the skis and you're good to go.