Okay I got it! For the custom buttons, you can use the custom code section. Configure your preferred buttons from here: https://www.addthis.com/get/sharing (Use “Disable and select your own buttons” option to hand pick the buttons)
Use the generated code in the “Custom Code” section in WordPress AddThis Share plugin option. You need the HTML part only.
For example, if the code generated from AddThis Site is:
<!-- AddThis Button BEGIN -->
<div class="addthis_toolbox addthis_default_style">
<a class="addthis_button_facebook_like" fb:like:layout="button_count"></a>
<a class="addthis_button_tweet"></a>
<a class="addthis_button_pinterest_pinit"></a>
<a class="addthis_button_google_plusone" g:plusone:size="medium"></a>
<a class="addthis_counter addthis_pill_style"></a>
</div>
<script type="text/javascript" src="//s7.addthis.com/js/300/addthis_widget.js#pubid=xa-517014c03ffc324b"></script>
<!-- AddThis Button END -->
you have to strip the javascript part and use the html for buttons as:
<!-- AddThis Button BEGIN -->
<div class="addthis_toolbox addthis_default_style">
<a class="addthis_button_facebook_like" fb:like:layout="button_count"></a>
<a class="addthis_button_tweet"></a>
<a class="addthis_button_pinterest_pinit"></a>
<a class="addthis_button_google_plusone" g:plusone:size="medium"></a>
<a class="addthis_counter addthis_pill_style"></a>
</div>
<!-- AddThis Button END -->
Considering the feedback from the support forum, we will be providing a more flexible configuration option (as we have in the AddThis Site) in this plugin soon. Till then, please use custom code to hand pick the buttons you wish to show in the site.