You’re correct: FusionAuth’s Lambda environment does not provide access to external libraries (including AWS SDKs or SigV4 helpers), and there is no secure secrets store available to Lambdas. That means if you need AWS SigV4 signing from inside a Lambda, you would have to implement the signing logic yourself and embed any required credentials directly in the Lambda code—this is generally not considered secure.
Also, if you are using FusionAuth Cloud, you cannot place Lambdas into your private network (for example, the same VPC/network as your API Gateway), so that option isn’t available in hosted deployments.
If you need this capability, the recommended approach is typically to move the signing and secret handling into a system you control (for example, a backend service that FusionAuth calls), rather than performing SigV4 signing directly in a FusionAuth Lambda.
Related issue tracking:
https://github.com/fusionauth/fusionauth-issues/issues/1629