I am using IBM's OpenWhisk service to stand up a micro-service with a REST endpoint. This expects Basic Auth in it's header when making a POST request to it.
Is it possible to add some custom headers in the Slack Outgoing Webhook settings page so that Slack can hit the OpenWhisk endpoint?
On
You can create a web action this will expose an API with no authentication required more info here https://console.bluemix.net/docs/openwhisk/openwhisk_webactions.html#openwhisk_webactions
Also there is an example using the Event API for a Slack App here: https://github.com/ibm-functions/composer/tree/master/docs/tutorials/translateBot#connecting-the-app-to-slack
Don't think that is possible.
If you want to trigger another service based on new messages in a channel I would suggest setting up a Slack App triggered by a message event. That Slack app can then post to your OpenWhisk service according to your needs.
Check out Slack's Event API for details.
This is also the recommend approach, since outgoing webhooks are legacy and should not be used for new projects if possible.