Like I said in your other question, there is no built-in way to modify the address bar. You will need to use a third-party program that runs in the background and modifies the address-bar's properties to adjust its length and hide the refresh button.
Unfortunately, I don't know of any such programs, nor can I find any. I have a tool I wrote myself that is similar to WinSpy++, but while both my program and WinSpy++ can be used to alter the length and hide the button manually, neither one runs in the background to detect whenever the address-bar is created and perform the modifications automatically.
One thing you could try is to use a hotkey/macro type of program that can let you set triggers to perform events, and set a trigger to be window created - address-bar...
and set the event to be hide refresh button; set address-bar length=...
This can probably be accomplished with AutoHotkey or AutoIt as well.
This is the AutoHotKey port of my C++ program to remove the refresh button. (It can be compiled and run in the background.)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; NoAddressBarButton.ahk (http://superuser.com/questions/444406/)
;
; This script hides the refresh button of the address-bar band of the Windows 7
; taskbar. It also extends the combo-box (edit field) to use the space of the
; refresh button.
;
; (cl) 2012- Synetech inc., Alec Soroudi
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
#NoTrayIcon ;No tray icon, duh
#NoEnv ;Not using environment vars
#SingleInstance Force ;Use only a single instance
#Persistent ;Using a timer loop; keep open
SetTimer, Run, 1000 ;Re-run the check every second
Run:
IfWinExist ahk_class Shell_TrayWnd ;Check if taskbar exists
{
ControlGet, tv, Visible, , ToolbarWindow323 ;Is refresh button visible?
ControlGetPos, tx,ty,tw,th, ToolbarWindow323 ;Get button width
ControlGetPos, cx,cy,cw,ch, ComboBoxEx321 ;Get combobox width
ControlGetPos, mx,my,mw,mh, msctls_progress321 ;Get address-bar width
if ((tv==1) || (cw<mw)) ;If button visible
;or resized (combobox is short)
{
Control, Hide,, ToolbarWindow323 ;(Re-)hide the refresh button
ControlGetPos, cx,cy,cw,ch, ComboBoxEx321 ;Get current combobox width
cw:=cw+tw ;Add the button width
ControlMove, ComboBoxEx321, , , %cw% , ;Extend combobox to include button
}
}