Using only the brake lever, separated from an integrated shifter/brake I have an old Shimano STX integrated shifter/brake. The shifter part is broken. 

Can I separate the shifter part, with reasonable effort, so I use only the brake and get a new shifter?

From what I could see, it is a single piece of plastic housing (I am not sure if there are tiny screws or rivets, perhaps hidden; I do not have access to the bike right now), so I would say no, but suggestions are always welcome.... Who knows. This shows the picture below.



EDIT: This question is related to Suitable Shimano integrated shifter/brake replacement for old STX

EDIT2: I found a couple of related posts

http://www.bikeforums.net/bicycle-mechanics/679944-can-you-remove-brake-levers-shimano-ef-50-integrated-shift-levers.html

http://www.bikeradar.com/forums/viewtopic.php?t=12966554

http://ridemonkey.bikemag.com/threads/can-i-separate-my-shimano-shifter-and-brake-lever.165662/
You can use the brake lever without the shift portion just by disconnecting the shift cable. Then, you can attach a bar end shifter or a downtube shifter or similar to shift instead. 

You won't be able to replace just the shifter portion of the brifter (without probably canabalizing another brifter anyway and actually manage to put the old one together). 

You can also buy a 7 speed or so brifter from Microshift still which is Shimano compatible, or the Shimano Tourney 7 speed brifter.