How to write unit tests for connectors?

I've a connector class which utilizes the wrapper utilities for HTTP connections.

ServiceResponse getResponse() {
    return connectorUtility.get(ServiceKey.MY_SERVICE_1_KEY)
            .addHeader("clientId", CLIENT_ID)
            .addHeader("Device-User-Agent-ID", duid)
            .routeParam("userId", userContext.getUser().getUserId())
            .routeParam("tuid", userContext.getUser().getTuid())
            .routeParam("siteId", userContext.getSiteContext().getSite().getId().getId())
            .withTraceContext(userContext.getTraceContext())
            .withObjectMapper(objectMapper)
            .asObject(ServiceResponse.class);
}

What's the right way to test right set of headers are passed to HTTP request? I want to get response "only" when right-set of headers, and only if URL is correct (with params passed). Also, I want my tests to fail if some one miss to add trace context (it can be null).

Should I use wiremock? Does it give flexibility to trigger when headers match?