FHU

I don't believe there are many (if any) that meet that criteria. Most of the FHU sites in Missouri's state parks are in the trout fishing areas but Arrow Rock State park might be of interest. Here is a list of all CGs and their offerings. linky

Cuivre River State Park near Troy Mo has some full hookup sites.

Corp of Engineers sometimes have FHU. However, do you really need a sewer hookup for 4 days? Just do a little conserving and I'm sure you can make it.