Using nginx $request_id for CSP nonce value: how to avoid caching it?

Question

I'm using the nginx $request_id for the CSP nonce value, but how can I get fastcgi_cache to bypass caching it?

I tried this above the location block where the variable is created, but it seems to stop all caching:

if ($request_id != "") {
    set $skip_cache 1;
}

To create the variable inside the block, I'm using:

fastcgi_param REQUEST_ID $request_id;

Thanks for any help.