Hi,
It's not that.
If you have both joomla and HikaShop recaptcha plugin, then when you are on the HikaShop registration page, only HikaShop's recaptcha plugin displays its captcha, since Joomla plugin doesn't support HikaShop's registration page.
However, when the user account is created, both plugins are triggered by the user creation process and the Joomla captcha plugin displays an error because its captcha wasn't displayed / validated on HikaShop's registration page.
So you want only HikaShop's recaptcha plugin.
Now, the fact that you have an error message regarding the captcha on the forgot your username/password pages is not something handled by HikaShop. So you have to fix that. You must have enabled something at some point to do that and it's not in HikaShop.
I would recommend posting about that on the Joomla forum so that someone who knows better joomla's recaptcha system can tell you where to look exactly.