Another possibility would be to create an abstract class with

sub dumper {
    die 'Dumper not defined in the abstract class!'
}
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then subclass it with MyClass::Dumper where you override the sub:

use Data::Dumper;
sub dumper {
    my ($self, @data) = @_;
    print Data::Dumper::Dumper(@data);
}
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If the user wants to use a different Dumper, they can subclass the abstract class with a different implementation of the dumper.