How do I manually update without using Drush nor Composer? Is it possible to upgrade Drupal from 8.3.7 to 8.4 without Drush or Composer? 

Even though I have used composer I am not comfortable with using terminal/console command lines operations. So far used composer to install and remove modules. That's about it.

Looked at manual update options. There are no instructions yet for this method. 
https://www.drupal.org/docs/8/update/update-core-manually-via-gui-option-1

This is what I am planning on doing. 

Download and extract Drupal 8.4 zip.


Backup database  through PHPMyAdmin and website before
proceeding. 
Put site in maintenance mode by going to
configuration -> maintenance mode 
Remove ‘core’ and ‘vendor’   directory project dir. 
Upload the core directory from the Drupal 8.4 version 
downloaded. 
Upload .htaccess,composer.lock and composer.json files from the downloaded Drupal to project. 
Upload vendor directory from the download
Drupal version to your project. 
Go to site.com/update 


Am I missing something? Or should I figure out the composer route?
The official update method is described in UPDATE.txt:

http://cgit.drupalcode.org/drupal/tree/core/UPDATE.txt?h=8.4.x

This is basically what you've described in the question. You don't need composer to update core.

If you want to switch your existing installation to composer a risk free way would be to start a new project, see Updating core with Composer doesn&#39;t work.