Your best bet may be to remove the toolbar completely and create buttons that do the same thing. Then you have the ability to hide the buttons when you do wish for them to appear.
You can also do this with custom menus.
If you have FMPro Advanced, you can use custom menus to assign the Find in the menu item to run your script. This behavior will be inherited by the find button in the toolbar. (ie - clicking the toolbar find button will now run YOUR script, same as selecting Find in the menu or typing CMD-F (mac)/CTRL-F (windows).
Thank you. I have Pro Advanced and the this specific solution is based on different custom menus (for different layouts).
This is how I solved it: I simply installed the "requests" menu set and made it only load in find mode. I had missed that there is a separate menu set for "new/delete/show all/etc" to be used in find mode.