OK, this isn't a way to automate, as you and I would like, but it's a workaround. It relies on the observation that one's Skype username is in the title of the Contacts Window. 
 The Contacts Window is in the scratchpad, so you can toggle its visibility with a key; the Chat Windows remain tiled. Thus, when you lay out the tiled Chat Windows as tabbed or stacked, you exclude the Contacts Window.
 # Skype.                                                                                                                                                             
for_window [instance="skype" title="G12ES"] floating enable, move scratchpad, scratchpad show;
bindsym $mod+backslash [instance="skype" title="G12ES"] scratchpad show;
 Unfortunately it seems one can't assign the floating scratchpad window to a workspace, but one can assign the tiled Chat windows to a workspace.
 UPDATE
 I have abandoned the floating window approach. I now (1) fire up Skype in a workspace (2) enter my special "workspace layout" mode (3) type 's k y' and hey presto I have the contacts window on the left and a stacking container on the left (a terminal). If I then (4) open a chat window, it appears stacked in the terminal container. This is a  vile hack ...
 mode "Layout" {
    # Skype.                                                                                                                                                         
    # https://faq.i3wm.org/question/2593/tabbed-layout-for-skype-chats/                                                                                              
    # The terminal acts as a stacked container for chat windows.                                                                                                     
    # The contacts window is moved to the right of the terminal.                                                                                                     
    # Chat windows are configured to appear inside the stacked container.                                                                                            
    # See "Define workspace layouts ..." elsewhere in this file.                                                                                                     
    bindsym s exec i3-sensible-terminal --title "Skype™ Chat"
    bindsym k layout stacking
    bindsym y [instance="skype"] focus, move right, mode "default"
    # Go back to normal.                                                                                                                                             
    bindsym Return mode "default"
    bindsym Escape mode "default"
    bindsym    Tab mode "default"
}
# Define workspace layouts in conjunction with layout mode.                                                                                                          
assign [title="Skype™ Chat"] sk
assign [instance="skype"] sk
for_window [instance="skype" title="Skype™ Chat"] move left, move left