It should be possible to hook into the <<MenuSelect>> virtual event bound to the popup menu but I am having a hard time figuring out how to do so...

Another less elegant way is to just poll the state of the -wrap option and do your callback when it changes.

use warnings;
use strict;
use Tk;


my $mw = new MainWindow;
$mw->geometry("200x200");
my $frame = $mw->Frame()->pack;

my $textbox = $frame->Scrolled('Text',
    -scrollbars => 'soe',
    -foreground => 'blue',
    -background => 'white',
    -wrap => 'none',
  )->pack;
$textbox->insert('end', "This is scrolled widget.\nThis is scrolled wi
+dget.This is scrolled widget"); 

my $wrapmonitor = $textbox->cget('wrap');
$textbox->repeat(100, 
    sub { 
        if ( $textbox->cget('wrap') ne $wrapmonitor ){
            $wrapmonitor = $textbox->cget('wrap');
            mycallback($wrapmonitor) #whatever
        }
    }
);

MainLoop;

sub mycallback {
    print shift, "\n";
}
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