I frequently get asked if there is anything that will make a person's dog shed less. And the answer is no. There is not anything you can feed your dog, put on your dog, bathe your dog with, etc that will eliminate shedding. It's biologically impossible.
Dog (and cat) hair grows in three phases: Anagen-the growing phase, Catagen-the in between phase, and Telogen-the resting phase. Telogen hairs are the ones that are falling out, or shedding. The individual hairs are not on the same cycle and thus some hair will always be in the Telogen phase. Occasionally a severe illness will push all hairs into the telogen phase and they will all fall out, but this is not a desirable way to end shedding.
Your best bet is to brush regularly and collect all the Telogen hairs in one spot. Then you can dispose of it before it gets dropped off all over the house!
Obviously some dogs (typically those that require routing grooming or clipping) such as poodles, bichons, and certain terriers don't shed as much. Their hair cycle and biology is a bit different but don't expect these breeds to never lose any hair. Remember, people don't "shed" but we still lose hairs just from regular "grooming!"
Shaving your dog (and I'm talking about the dog that are not meant to be shaved) does not make your dog shed less. It makes them shed shorter hairs. These hairs are often them embed themselves in clothing, furniture, etc and are near impossible to get out!
Now if you want to shave your dog for other reasons that is your prerogative. But I'm going to come right out and say it (and I don't mean to offend anyone) but I hate, hate, hate when people shave dogs not meant to be shaved. Think Goldens, Shelties, Border collie, Collie, Aussie, Pyrenees, Husky, Malamute, Lab, German Shepherd, etc. Yes, I have seen people shave short haired dogs like labs. I don't understand it, but I see it. Be aware-repeated shaving of these dogs often causes the hair to eventually fail to regrow like normal. It will be fuzzy, short, dull, patchy and irregular in length. It's easy to spot a dog that has been repeatedly shaved-in my opinion, they look terrible. Sort of like what you would expect a hypothyroid dog on cheap dog food to look like. So consider yourself warned!
As far as shaving your dog to keep them cool the jury is out. I have read lots of threads on shaving on a well known veterinary forum and the opinions vary widely. I will stick with recommending not to shave and encourage use of the good old AC but others will likely have another opinion.