[Test Proxy] Skip sanitizer removal if test proxy isn't running (Azure#35526)

Author: mccoyp

tools/azure-sdk-tools/devtools_testutils/sanitizers.py

@@ -484,6 +484,9 @@ def remove_batch_sanitizers(sanitizers: List[str], headers: Optional[Dict] = Non
     :type headers: dict
     """
 
+    if is_live_and_not_recording():
+        return
+
     data = {"Sanitizers" : sanitizers}
 
     headers_to_send = {"Content-Type": "application/json"}