It sounds like it’s integrated into Kagi’s main results and you can use the API to reference only the small web results, but I also don’t see a way for a Kagi search user to toggle “small web” results as a lens or whatever. I assume and hope that may be added in the future.

You are right, this is a good idea and I encourage you to post it on kagifeedback.org as a feature suggestion.

In the meantime you can toggle the 'non-commercial web' lens which will include KSW (and some other things).

That was a deployment issue (https://news.ycombinator.com/item?id=37420695), it's working now.