You can use the “Add a Gadget” feature to add WidgetWhats code to your Blogger site.
First of all, from the Blogger dashboard go to the “Layout” menu option, once there click on “Add a Gadget” in the “Sidebar (top)” section and choose an HTML/Javascript one.
Configure the Gadget as follows, the Title field can be left empty, in “Content” paste the code you have obtained in WidgetWhats, then save the changes. You now have your WhatsApp widget installed.