As far as I know, you can only edit styles using the desktop program, but if you are at an institution with Endnote, the “local EndNote online Administrators” also have the ability to update Styles for their site if EndNote online access is provided by Web of Science. If you have EndNote online access through your institution, you can contact your local Administrator to update existing Styles or upload new Styles.
Your EndNote online Administrator should be able to upload the output style following the instructions below,