I haven't actually tried this, but in theory it should work. (You'll have to play with the layout of the buttons of course)
Also keep in mind that the data I have is from WLM 9, so it might be a little different, but should be similar.
See the following image:
Go to the 4004 -> 920 section (Conversation XML area)
The send and search buttons are in a container with the atom id of "sendandsearchbtns".
You will want to move this section, included this element's parent, to the bottom of the "inputareacont" element's children. You will want to change the layout from client to right so that it the buttons go to the right.