How do I get the blog teaser view display on a content type?
Short answer:

Yes, you could do it without views. But, it wouldn't be ideal.

Long answer:

Display suite module will let you control the display of the particular content type and its fields. It won't allow you to control the display of a different content type from the other.
E.g. For your my-content-type, it will allow you to change the display settings of the fields of this content type.

If you wish to display teasers of nodes of the blog content type, on the node pages of my-content-type, you will have to do the follow the steps below:  

Without views:


Create a custom module.
Load the blog $node using node_load on my-content-type node page.
Using node_view on the $node get the node in the teaser view of the node.
Use drupal_render to render the loaded teasers in a custom block created using hook_block_info.
Place this block in an region only on the my-content-type node page.


With views:


Create a view block of content of type blog.
Select the display method to be content, and select teaser from the settings.
Apply additional settings (filters, relations) as required.
Place this block on the node page of my-content-type.


In other words you let views build your query for you. And you also get an additional advantage of using other features provided by the views module like caching, etc.