Not really… an least not easily, do_shortcode is indiscriminate. If it’s a registered shortcode WP will run it.
It could be done with some work. You’d need to first build your own shortcode function/filter and use this instead of the WP hook. Look at the core function do_shortcode(). You’d pretty much need to do everything that function does, and possibly some of what the called functions do, yourself and build a “White List” to check shortcodes against to see if they should be run or not.
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