I had a hen break her leg and it was actually dangling. The break was so splintered that I was afraid I would not be able to set it but I actually was able to use layers of paper tape to make a cast and when I unwrapped the leg after a month she had healed extremely well. I kept her in a tub inside so she did not have to move to eat or drink and I splinted the leg to her body for the first few weeks before I let her put weight on it.
If you can feel a break and set the bones you can heal a broken leg. If it just feels swollen it could be soft tissue damage. You can split it for support if that helps or just let the duck favor it and see if it is able to gradually put weight on it.
I have a hen now that carried one leg behind her and I could not feel a break so I have just let her limp with it. It is getting better where she has it under her more so I think it is healing but soft tissues can take longer to heal than breaks.
I tore my ankle tendon 8 months ago and I walked on my ankle for 6 months thinking it was a torn ligament until I had an MRI and discovered the tendon tore so bad that it will not heal without surgery. I will have surgery on the 26th, 9 months after my injury, and then it will still take another 6 months to heal following the surgical repair.
Since your duckling is using the leg for support, you may not need to do too much for it but you could tape the leg in order to help stabilize the tendon during healing. You could also do nothing and keep an eye on it to make sure it is getting better and not worse. Sometimes swellings will show bruising or feel hot to the touch but it looks like it is just swollen so hopefully it is only a sprain.
Have you checked the toe functioning to make sure nothing is dislocated?