Unfortunately, one more point to consider if fretting about the legal technicalities of creating a baby pool sized wading area for the ducks: If the stream is a “dry run” as we call it around here,(i.e., it is normally dry except during rain events), it falls under more lenient regulatory restrictions than a “wet stream” (carries water flow all the time).
Just make sure those critters are licensed and registered with the proper authorities, their feed is non-GMO, and you clean your rain gutters twice a year.:rolleyes:
Why don’t you just dig a hole?
That, or just use local/natural materials, and make it look non-man-made. Hawaii has no shortage of rocks and sand - you could probably get what you need in the trunk of your car from the nearest construction site - probably the same amount of material as going to the hardware store. If anyone were to question you, you could just say it has always been there/the Hawaiians built it eons ago.
Dig a hole in the stream? It would quickly fill up with silt.
Dig a hole in the ground? The soil here has a high percentage of volcanic cinder and drains quickly and they shit in the water constantly.
The ducks love kiddie pools, but they shit so much in them that I can’t keep up with the cleaning.
The stream pond idea eliminates the cleaning problem.
Based on your comments, this may not work, but I was going to suggest digging a hole down but using a PVC pond liner over the volcanic cinder. It’s maybe not a cheap as the concrete option, but still only $34 for 7ftx10ft sheet, and possibly a lot easily to lug over than the cement.
The easiest course of action might be to get rid of the ducks! 
Good luck w/ whatever you choose to do. Just wanted to mention my experience when a family member was caught altering water flow on his property. Was a major hassle. But if you feel you’ll never get caught, and since there are no people downstream …
If you want your dam to last longer than a couple of years, you should definitely do more than just plop some bags of cement into the water.
Simple illustration of what happens to a river with a low head dam.
Basically, it doesn’t take long for the sediment to pile up against the dam.
Sediment management is a huge, huge problem with dams, even government-built ones with billions in funding. It takes careful management and construction to deal with sediment build-up. A silt-trap is a good first step, though there is going to be a lot of sediment that’s traveling in the water that won’t reveal itself until it hits the dam wall.
Interestingly, waterfowl excrement can also help seal the bottom of your reservoir. Frank Herbert (of Dune fame) did just that on his property, creating a pond that raised the local temperature a slight amount. Insert your own “something something must flow” joke here.