You may have to be creative with this issue. I would start with your doctor and see which foods in their original form are without salt or little salt and have less fluid content. Get very educated about the foods that are good. Perhaps a nutritionist and/or dietician could help, here.
Rather than relying on the chefs totally I would stick with natural foods. Go to places with a salad bar and choose safe products from that area perhaps. Keep in mind that lettuce and tomatoes, for example, have a liquid content. Carrots probably have less liquid. Some fruit could be okay, too, but if you need to watch water content you don't want watermelon, for example. Most fruit has a liquid content; so, I'm not totally sure how critical this would be, either. Again, this is where your doctor comes in. You need to know which foods are better. Getting protein may be an issue, but a hard boiled egg could be okay. This has to be checked out thoroughly with your doctor as to which foods are more safe. Maybe, you can get a basic sandwich for him at a restaurant that meets your needs. Overall, I can see this being very difficult to accomplish at Disney restaurants. I just wouldn't trust the situation even if the chef seems nice about it. There are some restaurants at Disney World that are not Disney owned; many of those restaurants are located in World Showcase in Epcot. I would even be more concerned at those places. If you have a good palette for a salt taste I think I would pre-taste all the foods he eats from a chef. If you suspect salt I wouldn't let him eat it. I'll give an example. I use very little salt at home and broccoli is one food that I can really tell the difference eating at home vs. in a restaurant. The restaurant broccoli always taste like it has too much salt.
Actually, if you really want a Disney World trip with him that is safe, then I would consider preparing the meals for him. This may mean you need a place at Disney with a kitchen. If you are on a budget then this may not be doable. There are offsite resorts with kitchens for much cheaper, but then you need to find one that has shuttle service to Disney. You may have to rent a car; so, you can get groceries and get to the parks.
Monitor his symptoms for fluid retention. Check for changes in his fluid status by weighing him daily and checking for swelling. You may have to take a scale with you. Call your doctor if you have unexplained weight gain (3 pounds in one day or 5 pounds in one week) or if you have increased swelling, for example.
I'm not sure if this trip is a good idea, either. I'm not sure if with more time that the doctor may relax some conditions, but it may be wiser to do a wait and see for a trip later in time. I would absolutely not go during hot weather times in Florida.