Thanks, Mark, that’s exactly the information I needed.
My quick and dirty solution was to open the applet on the user’s mac in Script Editor. Then save it as an app. Then run it, three times, and after each run going into the System Prefs app and giving it permission to control Finder, Transmit and Text Wrangler.
Since I hadn’t edited this applet since 2015, I don’t expect I’ll have to repeat that process anytime soon.
But, with my company fully supporting macs agains (yay!) I think I’ll see more people trying to run my scripts on newer systems, so I’ll need to get the paid apple ID and start code signing.
It’s probably worth pointing out that with 10.15, and with 10.14.6, standard code-signing does nothing in terms of Gatekeeper. (I suppose it helps if you’re only distributing to users running older systems, but that’s just leaving traps for later.) You really need to move to notarization if you can. And the latest version of SD Notary should run under 10.13.6 and later.