Because security is so vital, and various people on these forums have been investigating whether different security plugins will work with CP, I reached out to the author of the MalCare Security plugin (it provides malware scanning, a firewall and some other features).
Here’s the thread: Support for ClassicPress | WordPress.org
So it seems that all should be OK with this plugin, certainly with V1 of ClassicPress.
It doesn’t work on localhost installations, only live domains accessible on the net (because MalCare servers initiate communication with the plugin for scanning), so when I have time I’ll set up a subdomain and give it a whirl.