I do not want to accept payments from my app so I do not need the Commerce API but I am having trouble authenticating via an iOS app without being able to define custom url schemes in the "Redirect URL" field.
According to Square's API documentation, OAuth is the only authentication scheme available however it restricts the "Redirect URL" to http://localhost or https:// only.
Most OAuth implementations allow defining custom schemes yourapp://oauth-callback instead of just using https://oauth-callback to implement this sort of flow on mobile devices (at least on Apple devices).