Duckiewuckie
Chirping
Squishy squashy yucky little duckies are the bestest 

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Do you have picture of the river rock by any chance? I want to take a look at size, and what is doable for ducks.I buy river rock at Lowes and put it around where their buckets are to discourage them mucking up the water but they still manage to muck it up. It's really easy for them to walk on though smooth and round
If you want to use gravel, the least expensive option suitable for ducks in our area is washed river rock http://www.whiz-q.com/product/gravels/50005YARD.html
As you can see in the photo, the pieces are rounded and safe for duck feet. Size will range from 1/2" to 3". This is big enough to discourage digging and swallowing. Unlike pea gravel, river rock will compact and provide a firmer surface for walking, which will make it more convenient when you do maintenance. Whiz-Q is in SE Fort Worth, relatively close to your location in Mansfield. Unlike some stone yards which sell wholesale only, they are set up for retail customers, don't mind you looking around, will sell you small amounts for samples, and can deliver.
If I wanted gravel in my runs, this is what I would use.
G/Mexican pebbles looks like the best option to me! I hope to get ducks in the future and I’d love to find some rock like thatOk. Here are my local rock options in order:
A: Colorado rock small
B: Colorado rock large
C: Torpedo rock
D: Arizona rock
E: pea gravel
F: Brazos rock
G: Mexican pebbles
So for drainage and waste management and smell is smaller better or larger?