I’m setting up 2 regional shopify sites. Should I consider canonical tags or/and use hreflang to ensure that search engines will send my users towards the right site.

The first store covers the Europe region. The second (and default) covers the remainder of the world.

Both stores are in English (UK), but their content will differ slightly (i.e they are not duplicate stores as such, and have different stock levels for example).

Currently Shopify includes the following tags:

<link rel="canonical" href="{{ canonical_url }}"> 

Which translates to:

EU Store:

<link rel="canonical" href="http://www.eu.example.me" /> 

Default Store:

<link rel="canonical" href="http://www.example.me" /> 

Should I alter these to include hreflang & canonical tags as well, and in which order should the hreflang tags be placed?

EU Store:

<link rel="canonical" href="http://www.eu.example.me" /> <link rel="alternate" hreflang="x-default" href="http://www.example.me" /> <link rel="alternate" hreflang="en-EU" href="http://www.eu.example.me" /> 

Default Store:

<link rel="canonical" href="http://www.example.me" /> <link rel="alternate" hreflang="en-EU" href="http://www.eu.example.me" /> <link rel="alternate" hreflang="x-default" href="http://www.example.me" />