The first method you mentioned is the canonical one. However, if you must do it on import, I would organize it as so:

package My::Singleton;

my $object = bless {}, __PACKAGE__;

sub import {
    shift;
    my %args = @_;

    $object->$_( $args{$_} ) for keys %args;

    return;
}

sub new { return $object }

# Your methods here
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