I wanted to do this a long time ago but I wouldn't trust my router with a Cloudflare API key. Paranoid or is there a way to limit that key to one domain or, even better, one DNS entry?
As the other commenter says, you can get pretty granular with the permissions. If you want to go even further, you can build a Cloudflare Worker that performs exactly the request that you want to do, and nothing else. Then you can configure your router to hit that instead of the API directly.