Hi,
Well, since you're using HikaShop's recaptcha and not Joomla's, you could activate the Redirect Joomla registration to HikaShop plugin via the Joomla plugins manager to use HikaShop's registration page only. That way, you'll be able to use the "after the address" mode of the plugin.
Alternatively, you could also activate the "invisible" setting of the plugin. That way, the captcha actually won't appear on the form unless Google thinks you're not a human (based on your behavior on the pages, where you click, etc). That would even help for your conversion rate since it's one less thing to do for your customers.