OK, I know what I did wrong.
The classpath setting for
javac doesn't need to include the location of the class that I'm about to create. So, not specifying the current working directory (the one where the class file I'm creating will be) is no problem.
java does need to know the location of all class files I want to use - including the location of the class I am executing (which for some asinine reason it can't find all by itself if it's in the current working directory). The solution then becomes:
java -classpath ".;.\whatever" SomeClass [someArguement(s)]