Thanks for the clarification on the platform Suarezventures.
I have worked with plenty of brands that have a similar setup on Shopify. They usually put the blog on a subdomain because Shopify's content management system - let's see, how do I say this nicely... sucks. These clients put up Wordpress on a subdomain. Some also put up a landing page platform like Hubspot or Unbounce to which they send paid traffic.
Your plan to put the eCommerce site on a subdomain has some benefits in that the content side won't be affected by future platform migrations on the eCommerce site. However, the content side will benefit the most from being at the main level with the homepage and most of the backlinks. Thus, organic search traffic to the eCommerce site could be harmed by this move. I normally wouldn't recommend it for that reason (because the business is eCommerce, which is what pays for the content) but in your case, it sounds like the eCommerce site doesn't bring in much traffic as it is.
Good luck. Let us know how it turns out.