Switch between AWS, Azure. Design pattern

We have developed some lambda function and deployed on AWS which are working fine, Anyhow, client is now planning for AZURE.

They may even switch back to AWS or any other vendor in future.

We have a separate maven project for AWS related stuff. Hence, our business logic and classes remains same.

What I have done is created a maven project and added individual lambda functions to this project as dependencies. Then made a factory class which will get impl based on property AZURE or AWS(using class.forName and reflection). SO, I can switch to Azure by just removing maven dependency and adding AZURE dependency.

According to picture my plan was to create new AzureUtils and AzureWrapper project and Directly use Azure Cloud, by switching cloud in cloudFactory which is present in Generic utils and that would even work hopefully (Not tested) AWS is working anyhow like that.

Now the problem is client does not want everything packed up in 1 jar, i.e no no to all lambdas in a single jar. He want some layer where the switching should take place.

Now Which design patter would be useful, what would be the approach.

Currently my Lambda function looks like below

public class Hello implements RequestHandler<S3Event, Context > {

    public String handleRequest(S3Event s3event, Context context) {

               .................
               call to business processor as in diag
    }
}

And azure function looks somewhat like a simple class with annotations

public class Function {

    @FunctionName("hello")
    public HttpResponseMessage run(
            @HttpTrigger(name = "req", methods = { HttpMethod.GET, HttpMethod.POST }, authLevel = AuthorizationLevel.ANONYMOUS) HttpRequestMessage<Optional<String>> request,
            final ExecutionContext context) {
        context.getLogger().info("Java HTTP trigger processed a request.");

        // Parse query parameter
        String query = request.getQueryParameters().get("name");
        String name = request.getBody().orElse(query);

        if (name != null) {
           call to business processor as in diagram
        }
    }
}

After all this I have only 2 questions

I would like to know first if the design in diagram is right thing to do.

And what my client is asking for a wrapper something magical which should handle both type of cloud implementations. is this even possible?

if possible guide me in right direction

Any help is greatly appreciated.