Completely remove custom post type permalinks ("One Page" website)

I created a one page style website that I converted to WordPress. The website include a blog, but I'm not using the usual WordPress way to display the post as I'm using a modal window appearing on click to displaying it. So basically I'm not using the Pages/Posts/Comments admin sections at all. Instead I decided to go with custom post types and create my own PHP loops. This is working pretty great for now.

But I have a problem with permalinks. Everytime I want to create a CPT, there's a permalink attributed to the "post". For example here's my CPT settings for a "carousel logo display" section (I use CPT UI plugin to create my CPTs, saying it just in case) :

    "labels" = $labels,
    "description" = "",
    "public" = false,
    "publicly_queryable" = true,
    "show_ui" = true,
    "delete_with_user" = false,
    "show_in_rest" = true,
    "rest_base" = "",
    "rest_controller_class" = "WP_REST_Posts_Controller",
    "has_archive" = false,
    "show_in_menu" = true,
    "show_in_nav_menus" = false,
    "exclude_from_search" = true,
    "capability_type" = "post",
    "map_meta_cap" = true,
    "hierarchical" = false,
    "rewrite" = false,
    "query_var" = false,

Which is working in a way. I mean that I don't have that mywebsite.com/CPT_Name/blablabla/ type of links anymore. But I still have something like mywebsite.com/?post_type=CPT_Namep=43 working instead (displaying my homepage), which is scary in a way.

I don't care if anyone goes on these links, because there is 0,1% of chance it happens (as of course I'll not publish/use these links at all). But I'm scared that Search engines get these permalinks in their database.

So basically, am I doing CPT the good way ? Do permalinks like the one I talked just before risks to appear on search engines ? Do I need to redirect these permalinks to my 404 page ?

Thanks a lot !