If your hosting enforces it to off, ask them if they allow an override with custom php directives.
They should, and if they don't, find a better hosting.
Thing about recaptcha (or any other code that require communication with the outside world) is that you only have few options, really: allow_url_fopen or cURL or some custom cURL library. No other way, I'm afraid. And, if you get compromised with some shell or malicious code, they will check both for presence, and if not found, they might implement the support in some other way directly in their code. If you shut your site/server from outside communication entirely (e.g. with firewall rules), it will be much more secure, but also very limited in what it can do. For example, you can whitelist some domains/servers, so that captcha always works, but that goes beyond simple forum reply's scope.