You can configure the list of supported browsers withoout need to recompile the program. Herefore, you must edit the file $(KDEDIR)/share/config/kurllaunch/browsers.rc.
This will has the structure of a common KDE-Config file. Enach browser will be represent by a group in this file. Every group can have following keys:
A text which will be displayed in the listbox of the configuration dialog.
Name of the execuatable. The entry for the browser will add into the listbox only, if the executable can be found.
Contains any optionals args which should be given to the browsers as parameters on the comandline.
If you create the configuration file, you should keep in mind, that the keys are casesensitve.