Cascade Delete - Delete entry from array

I am attempting to delete records in an array during a cascade delete function. This is largely a cleanup activity, but we have a custom table that has an array in it. 

I have the cascade delete working fine agains other (non-array) data sets, but while I can see a number of ways to do it, I am wondering if I am overthinking it. Does anyone have a recommended way to do it?

it seems I would point the 'target file' at the custom table we use, but I am wondering if it would make more sense to use a regular expression or if I should run it from javascript?

Once the operator name is deleted from the table, I need the operator name removed from the array in the secondary table (I actually have a couple of these tables, but once I have a solution for one it should work identically for the others as they are constructed very similarly).