You could try taking a look in the system properties under System > Management > System Properties. Depending on the implementation, the code is sometimes stored in a system property. This is also actually where the code is saved when entered from System > Settings > Third Party Analytics. Perform a text search from your browser for your tracking code ID if there are many properties listed and you can't quickly scan through them.
Otherwise you are correct that the code was most likely placed in the theme. You can view the theme files at System > Settings > Themes if you have appropriate access.
I was able to locate the file in Themes, which I pulled back to make the necessary updates.
Appreciate the assistance.