You may need to take a look at the documentation for that printer and your cash drawer. What part of the printing process opens that drawer? This sometimes is due to "printing" a specific set of control characters as part of the print job and if you can identify them and not "print" them, the drawer would remain closed.
But this is a wild guess on my part as I have not worked with this hardware and the drivers that come with it.
Just to make sure: The driver for the TSP100 has the option to open the drawer - this one is not checked in that script?
I'm using an epson thermal printer and the option to open the drawer is configured at the software driver and I think applies to all print jobs. Most restaurants have a separate kitchen printer just for food orders. I'm assuming in your setup it's the only printer and the cash drawer is connected to that printer. If there's no option to control this behaviour via a script then a second printer is your best solution.
we got both - Star TSP100 and Epson TM-T20, all USB printers with driver for OSX. On both, one can specify ('printer set up' script step) if the drawer should open or not. So, we have Scripts to open the drawer only, to print, to print AND open the drawer. This information is stored inside the script - only Problem was, that there was a 'little bit of paper feeded' when the 'drawer open only' script was fired..
But I agree - a second printer is a good idea.