You are right, "No sé qué ponerme." means "I don't know what to wear.", or it literally means "I don't know what to put on."
You can also say "No sé cómo vestirme." (I don't know how to dress up.), however the first option sounds a bit more common.
And the explanation you gave is also correct.
qué + inf = what to do
cómo + inf = how to do
Also, if you want to say "Tell me what to do.", it would be "Dime qué hacer."
BUT if you want to say "Tell me what to wear.", instead of saying "Dime qué ponerme" you should say "Dime qué me pongo."
And back to the original sentence, although the natural version is "No sé qué ponerme.", grammatically it is also correct to say "No sé qué me pongo."
beauties of the languages, right? :)