Sounds like a perfect application of a hydraulic trash pump. Most industrial models are very heavy, cast iron which makes it difficult to handle. Mud doesn't flow so you need to move the pump as you progress.
Now there is a trash pump that handles mud just fine and is quite lightweight. Made by Stanley, the hinge/hardware people. Urethane body so it is light. You also need some hose, I suggest a good, lay-flat because rigid hose is HEAVY. And 2 hydraulic hoses, about 50 feet long, depending on your HPU. I suggest at least one set of zero loss QD's to make it handy. Make sure the hoses don't leak.
Now for the HPU. You need 5 Hp, minimum and you need a gas-powered model. Look for logsplitter equipment. 2000 PSI is plenty, 1800 will work just as well. Mount the HPU in a boat and moor it with lines from the banks to lay out a grid. Run the lay-flat hose to a level area with a double silt fence to capture the muck. Pack straw between the two silt fences. You might need to stop the dredging operation if the silt pond fills more than halfway as the pressure will cause seepage of silt.
For hydraulic oil, use Enviro Rite if you value the fish or have tree-hugging neighbors. This oil is certified non-toxic to fish and despite your best measures, you will have leaks. Believe it or not, it actually sounds like you might have compliance issues with the Clean Water Act. Using the above procedures will help with compliance but it isn't complete.
Hose-handling is going to be the biggest problem. Do NOT use rigid hose. And depending on the silt, the lay-flat will eventually wear out. But if you want to save money, get a large power steering pump from the junkyard, hook it up to a 8 Hp gas engine and make a tank for the hydraulic fluid. You will not need a big tank, just a gallon but be careful when priming the lines as it will drain the tank. Once the lines are full, the zero loss QDs will keep the prime. See the many DIY sites on the web for home log splitters. They will fill in the details.
Get abrasion resistant hoses for hydraulics. They will be abused. Stay away from the lightweight hoses as they kink.
Here is the pump: TPO3
www.stanley-hydraulic-tools.com/Hand%20Held/Pumps.htmFor the weeds, you need to kill them before you can do hydraulic dredging. Coppersafe is a good brand. It is harmless to fish but will kill snails, clams and the like.
Dammit, I keep on editing this response...make double damn sure to secure the hoses well. This includes "whip-stops" on all connections. A hydraulic "fuse" in both lines is another good idea. These stop flow if a hose breaks.
One final note. The TPO3 Stanley comes with a perforated plate for the base. If you shroud this baseplate so all water/muck must flow through the holes, you will get better performance but you might have to clean the plate often.