That did not add a lot to the load time of the website, but it did add something, and forced users to make yet another request.
I stumbled upon Social Media Feather after some digging around and it appeared to be exactly what I was looking for in first place. Part of the plugins descriptions contains this paragraph:
The primary goal behind the plugin is to provide very lightweight WordPress social sharing and following that doesn’t add any unnecessary burden to your site and especially on your users.
What sets WordPress Social Media Feather aside from the plethora of other social sharing and following WordPress plugins is its focus on simplicity, performance and unobtrusive impact.
I ran tests on a local WordPress development environment and came to the conclusion that it indeed was as lightweight as the developer claimed it would be. It did not make external requests, and loaded only a couple of small social media icons on pages where it displayed the sharing options.
The plugin can display sharing and following buttons on the blog. It usually makes sense to display sharing buttons on post pages, and follow buttons somewhere else to avoid confusion. The sharing functionality works nearly out of the box, but if you want to make use of follow buttons as well, you need to add the social media pages that you want followed in the settings.
Here you can also modify share links and titles for several services, change icon appearance, or add extra CSS styles to the icons.
The sharing buttons are not displayed by default, and you need to enable that either in the options, by checking the "display sharing buttons" preference, or by adding the plugin call to your WordPress theme template files directly. The plugin supports shortcodes as well that you can add to widgets or in posts directly, if you prefer that. I have used a shortcode to display the follow buttons on the right sidebar.
All functionality up to this point is free to use. The author has made available add-ons for the plugins that are not free but extend the plugins functionality. You can buy icon packs, a grey fade add-on, or a light prompt add-on which loads overlays with options to like, send or share when a user clicks on a social media icon. This will also display the number of likes a post has received then which the default button listing won't (since it is static).
Without that add-on, users are always redirected to a new tab page where they can enter a comment and click on the share button.
The plugin is bare bones in comparison to sharing plugins or scripts that display the like count directly on the site. That comes as a price though as contents need to be loaded from various Internet sources which slows down page loading times.
Not loading scripts directly has a positive effect on privacy as well as Facebook, Google or Twitter do not get to know that you have visited a website on page load.
I have removed the big follow boxes on the sidebar as well, and replaced them with the plugin's follow icons instead.