If you cancel the dialog, the $colour variable is undefined. You then try to set the -background and -activebackground to an undefined value. CRASH!!

You need to check that $colour is defined before using it.

use strict;
use warnings;

use Tk;

my $cfg;
my $font_colour;
my $wd = MainWindow->new();

$wd->Label(
  -text    => 'Color',
  -justify => 'right',
  )->grid(
  -column => 0,
  -row    => 4,
  -pady   => 20,
  -padx   => 20,
  -sticky => 'e'
  );
my $colour_button = $wd->Button(
  -width   => 6,
  -command => sub { $font_colour = colour_picker() },
  )->grid(
  -column => 2,
  -row    => 4,
  -pady   => 20,
  -padx   => 20,
  -sticky => 'e'
  );

if ($font_colour) {
  $colour_button->configure( -background => $font_colour, -activebackg
+round => $font_colour );
}

MainLoop;

sub colour_picker {

  my $colour = $wd->chooseColor( -title => 'Color Picker', -initialcol
+or => '#000000' );
  $colour ? print "Colour chosen: " . $colour . "\n" : return;
  $colour_button->configure( -background => $colour, -activebackground
+ => $colour );
  return $colour;

}
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