Disable Ctrl-X / Cmd-X cut unselected paragraph

This can be tackled by opting for a non-Templater solution in the form of a command of a pseudo-plugin, using the so-called User Plugins plugin.
Create a .js file (e.g. ‘Override built-in CTRL+X behavior.js’) with this content:

module.exports = {}
module.exports.onload = function(plugin) {
    plugin.addCommand({
		id: 'cut-override',
        name: 'Cut override',
        callback: () => {
            const editor = app.workspace.activeLeaf.view.editor;
            const selection = editor.getSelection();

            // If no text is selected, do nothing
            if (!selection) return;

            // If text is selected, cut it and notify the user
            editor.replaceSelection(""); // Cut the selected text
            navigator.clipboard.writeText(selection).then(() => {
                new Notice(`Text cut to clipboard:\n${selection}`, 3000); // Notify for 3000ms
            }).catch(err => {
                console.error('Could not copy text: ', err);
            });
        }
    });
}

Add in the settings of User Plugins the folder where you keep your script files (.js), and then you can toggle this script on.
From this point on, you have a ‘Cut override’ command registered through the User Plugins helper and can bind CTRL/CMD + X to this command.
The plus of this method is that you will be no longer reduced to being able to use the script in the main editor area but anywhere at all without errors.