In place of

$self->{m}->($self,@args);

would you like $self->m(@args)?

All you have to do is cover up the syntax you dislike with a wrapper, like so:

package foo;
# dispatch table
my %m_implementation_for;

# wrapper
sub m {
    my ($self, @args) = @_;
    my $implementation = $m_implementation_for{$self};
    $implementation->($self, @args);
}
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Afterthoughts: or more tersely,

sub m {
    my ($self, @args) = @_;
    $m_implementation_for{$self}($self, @args);
}
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To be still terser, replace the implementations with closures:

my %m_closure_for;

# after the implementations have been defined
foreach my $object (keys %m_implementation_for) {
    $m_closure_for{$object} = sub {
        $m_implementation_for{$object}($object, @_);
    };
}

# terser wrapper
sub m {
    my ($self, @args) = @_;
    $m_closure_for{$self}(@args);
}
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