the code added to both short-CUTr versions

!g:: ; = [ALT] + [G]   or ~lalt & g::
clipboard =  ; empties the clipboard
send ^c  ;= [ctrl] + [c] copy to clipboard
run http://google.com/search?q=%clipboard%
return

Option: you can change the tld .com to .xy and you can add more parameters to the search url

how to:
→ click the H tray icon →scroll down to the bottom
or faster:  CTRL + F   "google" [OK]