My understanding is that you can bathe a dog in any soap or shampoo -- any suds will kill fleas if you lather them up and leave them soapy for 7-10 minutes before rinsing them off. A flea shampoo will have chemicals that, in addition to killing extant fleas, will repel fleas for longer, after the bath, if you don't mind exposing the pups to those chemicals. But really, fleas die and will drown in any soapy water, given a good enough lather and time.
Then, I'd let the pups have a good soak in an oatmeal bath. You can either buy fancy Aveno colloidal oatmeal bath powder, or you can make your own by just putting some regular oats in a blender and turning them into powder. Sometimes, I have put regular oats into a long gym sock, then tied off the sock. I fill the tub with warm/hot water and let the sock soak through. After 10 minutes or so of "steeping" I squeeze the sock to get the gooey, liquidy goodness from the oats and swish it through the bathwater. The more cloudy/oaty the water, the better. After a good soak, rinse them off well. This will really soothe their skin and should reduce scratching dramatically. Even if you don't bathe/shampoo them every few days, you can give them an oatmeal soak and rinse them off. This will reduce the itching.
Then, I'd recommend going with the spot-on flea stuff -- but generally you don't apply that until 3-4 days after bathing. It IS safe for pups, as indicated on the box.
You'll also want to be super careful about not introducing fleas into a non-flea-infested area. If you bathe the pups to kill the fleas on them, then give them a medication to kill future fleas, you should be okay... but not if they go back to the flea-infested environment. My understanding is that Frontline and Advantix and the like only kill fleas after the fleas have bitten the animal. Unless you address the problem of their environment, they may continue to suffer.
Best of luck! You're a good person to undertake it.