Hi,
So adding css properties in this css file will potentially hide the add to cart and add to wishlist buttons only in "print" context.
That means that the css will be used when trying to print the page, using the print tool of the browser.
If you want to hide the buttons directly in the popup, so you need to have a css file called only in the "tmpl=component" context, and this is handled (or not) by your template, we can't really give you the exact solution as it really depends on your template.
The best would be to contact your template provider directly to know on which file apply the css.
Then the css will be really simple, it only needs to be something like:
.hikashop_cart_button{ display: none;}
If you only need the print context, so buttons displayed in the popup but no when printing, so in any css file of your template you case use a media query:
developer.mozilla.org/en-US/docs/Web/CSS/@media