This can't be done by Kagi itself, maybe this could be implemented through their Browser Extension, but I don't think that the browser extension should implement something like this.
And custom bangs can already be created https://kagi.com/settings?p=custom_bangs
which do not support the %s parameter
This does not make much sense, a website does not need to support some parameter, %s is just a placeholder for your search text, and Kagi will replace it with your search text after the bang, for example https://example.com/%s
would become https://example.com/your search term
, maybe you mean websites which do not have the search text in their URL?