You may want to look into AppSync from AWS. It will handle a lot of this for you; authorizers, querying DyanmoDB, etc.
I've built Lambda APIs using Apollo GraphQL and exposed them through API Gateway. I then used Apollo's schema stitching to connect them together. There's one really important caveat here: It's slooow. There's already a speed penalty with API Gateway and while it's acceptable, imagine jumping through multiple gateways before returning a response to a user. You can cache the schema which helps a bit. Your tolerance will depend on your app and UX of course. Maybe it's just fine - only you (or your users) can answer that.
That note aside, the way I handled auth was to accept an Authorization header and make a check manually. I did not use any custom authorizers from API Gateway. I was not using Cognito for this so it talked to another service. This all happened before the resolvers. Why are you looking to do the authorization in resolvers? Are there only some that you wish to protect? Access control?
It may not be best to add the custom authorizers to API Gateway in this case...Because you're talking about performing this action at the resolver level in the code.
GraphQL has one POST endpoint for everything. So this is not going to help with configuring API Gateway auth per resource. That means you're now beyond API Gateway and into the invocation of your Lambda anyway. You didn't prevent the invocation so you're being billed and running code now.
So you might as well write your custom logic to authenticate. If you're using Cognito then there is an SDK to help you out. Or take a look at AppSync.