Custom Post Type – capability_type

A question,

The capability_type feature of a Post Type can be set to ‘post’ or ‘page’.

If I understand this correctly Pages can’t have Tags or Category taxonomies assigned to them but Posts can.

What to do if you would like to hook into a Post Type created by some other plugin developer?
I see this plugin developer has used:

'capability_type'    => 'page',

And I already have coded my taxonomy (cats) that hooks into his Post Type. Everything works tho, the categories can be created and I can show them front-end but there is just one single problem I can’t delete/remove the created categories because there is no menu-item showing up where you can edit/add or remove categories.

What to do ?

I’ve study his code and I see this:

register_post_type( 'mycred_badge', apply_filters( 'mycred_register_badge', $args ) );

If i’m not mistaken I can use that apply_filter ‘mycred_register_badge’ function to change the default page capability_type to a post capability_type but I’m afraid it will break everything because I already have created content in this Post Type when the capability_type was set to page.

Can somebody give me advise?