Add reCaptcha for just 1 page ?

Hi anyone, Good Morning.

I have a page called ‘ daftar ‘ for a visitor to create an account ( so they don’t have to do this on wp-login.php?action=register )

on that page, there are 3 inputs. Username, Email, and Password. and 1 button submit. I can do that on that page because there is shortcode [register_form] available from its wordpress theme. And these inputs are created inside momizat_function.php

What i want is, after i’ve succeed add reCaptcha to that page, i would redirect wp-login.php to that page, so visitor won’t see any wp logo or knowing that i’m using wordpress ( for a security reason ) and i want to stop from get user register spamming.

Now the question is how do i add the reCaptcha only on that page ?
i have read something on reCaptcha offisial site, or in someone’s blog that need to put the snippet before the </head> tag in html.

if i edit the html index for the theme that i used, and add the <script src=’https://www.google.com/recaptcha/api.js’></script&gt; before the </head> section. ( eventho i don’t know how to ) will it slowing or reduce my speed site ?

thanks, please forgive my english.