The first thing you should do when trying to speed something up is profile it (with something like Devel::DProf) to see what's taking it so long. If it's loading all the modules, something like pperl or a Perl compiler will help. If it's loading the data, maybe a different data structure would help.

In general, getting your users to minimize your app instead of exiting it should help no matter what's causing the slowness.

You probably need to intercept the window manager's close command..

#prevents mw from closing and iconifies instead
$mw->protocol('WM_DELETE_WINDOW' => sub {  $mw->iconify });
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For sleep, maybe something like this

tksleep($mw, 100);

sub tksleep { 
  # Like sleep, but actually allows the display to be 
  # updated, and takes milliseconds instead of seconds. 
   my $mw = shift; 
   my $ms = shift; 
   my $flag = 0; 
 
   $mw->after($ms, sub { $flag++ }); 
   $mw->waitVariable(\$flag); 
}
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use Storable;

my %spreadsheet_data;

if ( -f $storage_file_name ) {
   %spreadsheet_data = %{ retrieve( $storage_file_name ) };
} else {
   # read in all of your data into %spreadsheet_data
   store \%spreadsheet_data, $storage_file_name;
}
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Cheers. :)

1. probably this will not be liked by others, but it appears that http://search.cpan.org/~vkon/Tcl-Tk/ have faster startup time and smaller memory footprint than perl/Tk
2. when some other (small) Tcl/tk application will be started, startup time of previous item will be a bit better yet
3. call update several times from different points of starting, this probably visually be faster.