You’re correct that there isn’t an easy way to do this through the Alerting API at the moment. This was recently captured in an issue on the Alerting repo in Gitub. The search and GET APIs are missing for destinations and need to be added. You can use that issue to track the progress of this change.
As a temporary workaround, you can try to query the .opendistro-alerting-config index directly using an exists query to filter out destinations.