Want to implement schema markup using google tag manager without disturbing the code,then yes you are at right blog.Google Tag Manager makes it easy to implement in just few steps.
Schema.org is a collection of schemas for structured data markup that helps search engines better understand content on websites
If you are new to google tag manager then just visit here how to implement http://nectarspot.com/how-to-install-google-tag-manager-on-your-wordpress/
If you do not have any JSON-LD encoding knowledge, then head on over to SchemaApp.com to use their JSON-LD schema generator tool. All you have to do is enter the properties you want to include in your schema markup (some are mandatory), then copy the JSON-LD code to your clipboard.
Now use google tag manager dashboard and create a new custom html tag
Now paste JSON-LD markup into custom html box
Next, you will need to create a new trigger for your tag to fire on. You’ll want to select the page views trigger from the list on the right-hand side of your screen. Name the trigger “Page View.” You can use this trigger for other tags, too (tags that require page views in order to fire).
Now publish the google tag manager container,and now quickly test your schema mark up using the Structured Data Testing Tool to make sure it validates