In theory it should be possible to use simple OOP to override the behaviour you do not want. However, I do not know how to get around the problem that the derived class does not export anymore.

package Mouse::Util::TypeConstraints::CarplessErrors {
    use Mouse;
    extends 'Mouse::Util::TypeConstraints';
    sub throw_error :method {
        my ($self, $message, %args) = @_;
        warn $message;
    }
}

package Foo {
    use Mouse;
    use Mouse::Util::TypeConstraints::CarplessErrors;
    enum 'ErrorMode' => qw<carp error both>;
    has 'error_mode' => ( is => 'rw', isa => 'ErrorMode', default => '
+error' );
}

Foo->new->error_mode('asdsdf');
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