Theme independent plugin by using default page template

Using default page template has the same issues than using single post template. It is true that usually page tempaltes has not post information like author, date and so on, but it is totally up to the theme developer. Even there are themes without page templates.

But if you want to force the use of the default page template for your custom post, you can do it (only if page.php exists in the active theme, of course):

add_filter( 'template_include', 'cyb_set_template' );
function cyb_set_template( $template ) {

    if ( is_singular( 'yourcpt' )  ) {
        $page_template = locate_template( array( 'page.php' ) );
        if ( '' != $page_template ) {
            return $page_template;
        }
    }

    return $template;
}

Note that this break WordPress template hierarchy. No theme could use single-yourcpt.php to build custom templates for your custom post type. Also, the only template required by a theme is index.php and there could be themes only with index.php template file.

The next snippet could solve the issue by looking for single-yourcpt.php file first, theme page.php, single.php and finally index.php (code not tested):

add_filter( 'template_include', 'cyb_set_template' );
function cyb_set_template( $template ) {

    if ( is_singular( 'yourcpt' )  ) {
        // Try to locate single-youprcpt.php first,
        // then page.ph
        $page_template = locate_template( array( 'single-yourcpt.php', 'page.php', 'single.php', 'index.php' ) );
        if ( '' != $page_template ) {
            return $page_template;
        }
    }

    return $template;
}