Thanks to John the set_column() method is now much easier to use. Nonetheless I discarded all approaches I developed in this thread and found the solution below which is much easier to comprehend, I believe.

#!perl -l015
use strict;

use Spreadsheet::WriteExcel;

my $arr = [
    [ "a11", "12", "a13" ],
    [ "a21", "22", "a23" ],
    [ "a31", "32", "a33" ],
];

my $outputfile = "output.xls";
my $workbook   = Spreadsheet::WriteExcel->new($outputfile);
my $worksheet  = $workbook->addworksheet("a test");

my $number = $workbook->addformat(
    font       => "Helvetica",
    size       => 18,
    num_format => "0.00",
    align      => "right",
);
my $string = $workbook->addformat(
    font  => "Helvetica",
    size  => 18,
    align => "left",
    bold  => 1,
);

my $format =
  [ [ $string, $number, $string ], [ 16, 12, 16 ] ];

my $line;
for my $row (@$arr) {
    $worksheet->write_formatted_row( 3 + $line++,
        0, $row, $format );
}
$workbook->close();

chomp( my $pwd = `pwd` );
my $file = $pwd . $outputfile;
$^O =~ /Mac/ and MacPerl::DoAppleScript( <<eos );
tell application "Microsoft Excel"
    open "$file"
    activate
end tell
eos

package Spreadsheet::WriteExcel::Worksheet;

my $width_is_set = 0;

sub write_formatted_row {
    my ( $self, $rowstart, $colstart, $ref, $format ) = @_;
    my @arr = @$ref;
    unless ($width_is_set) {
        for my $col ( 0 .. $#{ @$format->[1] } ) {
            my $colwidth = $format->[1][$col];
            $self->set_column(
                $colstart + $col,
                $colstart + $col,
                $colwidth, undef
            );
        }
        $width_is_set = 1;
    }

    for my $col ( 0 .. $#arr ) {
        my $colformat = $format->[0][$col];
        die "parameter error: no format objects specified\n"
          unless ref $colformat eq
          'Spreadsheet::WriteExcel::Format';
        $self->write(
            $rowstart,  $colstart + $col,
            $arr[$col], $colformat
        );
    }

}
[download]