For what it is worth, I'll tell you what I would do.
Firstly, I'd consider relying on Delphi's power to read the clipboard.
Say I can't do it for some strange reason, this is what I have tried with Adobe Acrobat JS following Max and Gilad answers.
Open Acrobat > Ctrl+J to take up the Console > clear the Console, write and mouse-select
app.getPath("user","javascript");
then Ctrl+Enter: you'll get a path to a local folder.
Go to that folder and create a new .js file whose content is
var myHighlightMenuItem = app.trustedFunction (function() {
app.beginPriv();
app.execMenuItem("Annots:Tool:HighlightMenuItem");
app.endPriv();
});
close Acrobat and reopen it. Create a blank trial PDF > add a button > insert a new Mouse-Up Action > Run a JavaScript, i.e.,
myHighlightMenuItem();
when you push the button, the highlighter will be activated. If you wish, you can have it activated as soon as the document opens.
To do the same in Reader: open in Reader the file you have just created in Acrobat and push the button. If you set Reader JS Preferences to show the Console on error, it will pop-up. Clear it and write
app.getPath("app","javascript");
follow instructions above to create the same privileged function to be used by Reader.