The term of the time for "drafted" soldiers was "conscripted". This means that they did not voluteer, but rather were required to serve under the conscription laws. The were exceptions to this required service, called "exemptions", but being a foreign citizen was not one of these exemptions! Your family lore is probably correct.

One who was paid to serve for another person who was required to serve was called a "substitute".

I have a couple of books listing Confederate Marines. I'll check for his name.