We built a similar proxy at https://wrapapi.com/proxy to allow users to record and replay network requests when turning webpages into an API. I think it's possible to have an end-to-end secure and never-written-to-disk pipeline, provided you trust the provider is doing what they're saying.

The secure pipeline we ended up using involves:

1. Having a HTTPS endpoint for the proxy

2. Forwarding the captures to you immediately via listening WebSocket instances

Note that because the server upon receiving a request can immediately push it to WebSockets instead of relying on polling, no storage is needed