Hi,
I do see it on your HikaShop registration form:
monosnap.com/file/XGYeZfdbyZnfhqOgRgLwqGdenoXcMU
Now, I see that you have a registration button on the top of your website which opens a registration form in a popup.
That's not something coming from either Joomla or HikaShop. It looks like it's added by a module.
I'm afraid that if you're talking about this module, it's normal you don't see the recaptcha there as it would require adding some code to the plugin to support it. We could potentially look into it if it's a generic extension (and not a custom made for your website), but we would need more information on which extension it it so that we can set it up on our end to see what can be done.