Setting up trpc behind AWS API gateway and authorizing using a lambda

Current setup:
- trpc api, containing both public an private procedures. Let's call them posts.list (public) posts.create (private)

- API gateway routes GET /trpc/{proxy+} and POST /trpc/{proxy+} that invoke a lambda handler for trpc (let's call it trpc.handler)

- Auth is handled inside of trpc.handler using a middleware that checks the token etc.

Setup I want:

- Extract the auth part into a different lambda (let's call it auth.handler)
- Only run this authorizer for the private routes.

As I don't know in advance what the request url might look like (e.g. it could be batched), is this possible to setup?