It isnt one shot thing.
I have wasted almost 1 hour finding the exact template that affects the shoutbox on index page.

Mine settings were style=2 and show only in index page at top.
ACP > Look & Feel > Your Skin > Templates > skin_shoutbox_hooks > hookGlobalShoutbox

Find This:
Code: 
<div class='category_block block_wrap'
Add After:
(In same line)
Code: 
style='width:YOUR%'
eg.
Code: 
<div class='category_block block_wrap' style='width:77%'>
Leave Everything else intact, but this only gonna decrease your shoutbox width, you need few more skin edits to bring that sidebar hook at top.

I guess it wont be so hard, but I will try that thing on tomorrow...
Demo:
http://SourceParadise.com
http://screensnapr.com/v/XbgpjK.png