As far as I know, there is no direct and safe way to selectively contains the dependent classes in a fat jar generated by the sbt-compile plugin.
First of all, you should understand that sbt plugins just provide a settings and jar files required to invoke methods in your project. It means that the dependent plugin is brought to your project with the pre-compiled jar file, which is determined by the version that you specified on your build setting (e.g., plugins.sbt in your project dir).
For example, the jars of sbt-assembly are brought to your project from this link when you specify that you want to use the sbt-assembly (although it is brought to your project when you use recent sbt version by default).
Therefore, at least you may have two choices to shrink your jar files.
Compile the jar file from the scratch
For the sbt-aws, its source code is provided on this link, so you may selectively compile the source codes to get the classes that your program is going to use.
Use the tool for shrinking jar file
There are several tools to shrink your jar file based on the dependencies. The most popular tool is proguard; it seems that there is a proguard support for sbt.
Warning
As mentioned in another stack overflow answer, selectively choosing some classes from the jar may cause your program crash depending on the input value and several other conditions. You've said that only 10 percent of the jar file is used, but you cannot ensure whether other classes are required from your code and library that your project depends on. When you use the tool for helping you to shrink the jar file, be careful when the program is security critical one.