There is currently no client side trigger scripting functionality in Integrity, the trigger scripting is all server side. (see https://www.ptc.com/appserver/cs/view/solution.jsp?n=CS84709 for the offical mention of this)
With that said, there are some ways to run external executables on the desktop through the "custom" action group of the viewset->customize menu.
It is also possible set up integrations with the integrity client via the command line, java or C apis, so you can run some custom app or script that performs its own business logic before sending the data to the client.
I recommend opening a support case to discuss your particular needs with a rep and see if they have any guidance. You also may want to talk to your sales rep to see if the Professional Services group can build something to assist if this is particularly critical for your business.
Hope that helps,