Z Test of Two Proportions with Small Populations

#1
This seems like a fairly basic question but is one that I'm having difficulty answering.

For comparing two proportions to test for significant differences, I normally use a standard two-proportion Z test. However, I am working on a project that is a special case: we are surveying a very small population of a few hundred people.

I know that for calculating the margin of error for a single proportion, you can apply a finite population correction which will alter the standard error for the proportion. What I need to know is: how can you apply a similar correction when doing a comparison of two proportions?

If I survey this group and get a set of responses one day, and then survey the same population and get a set of responses to the same questions on a different day, how do I account for the small population size in testing for significant differences between the two samples? Is a Z test even the right test in this case?

Thanks!