When stating a hypothetical situation, "would" is most commonly used.
If I had a girlfriend, I would take her out dancing every weekend.
It isn't wrong to say something like:
"If I had a girlfriend, I could take her out dancing every weekend."
But these are two different statements. The first says "if A is true, then I will do B." The second says something more like, "If A is true, then I have the opportunity or ability to do B, but I may or may not do so."
When talking about past situations like the polio vaccine where something's ability or capacity is known because it happened, "could" doesn't make sense. It is true that Salk's vaccine has prevented millions or even billions from being stricken by the disease. So, since you have set up a hypothetical, use "would" to complete the statement.
If Salk had not invented his vaccine, many more would have suffered from polio.
It is possible to use "could" but only in cases where, for example, one past event relied on another past event:
If the Wright Brothers had not invented the airplane, modern transcontinental travel could never have been possible.
But even here, "would" works just as well.