diff --git a/jupyter_client/session.py b/jupyter_client/session.py
index c387cd06..f3e7afca 100644
--- a/jupyter_client/session.py
+++ b/jupyter_client/session.py
@@ -28,6 +28,7 @@
 
 # We are using compare_digest to limit the surface of timing attacks
 import zmq.asyncio
+from jupyter_core.utils import run_sync
 from tornado.ioloop import IOLoop
 from traitlets import (
     Any,
@@ -812,7 +813,13 @@ def send(
 
         if isinstance(stream, zmq.asyncio.Socket):
             assert stream is not None  # type:ignore[unreachable]
-            stream = zmq.Socket.shadow(stream.underlying)
+
+            async def _send_multipart(*args, **kwargs):
+                return await stream.send_multipart(*args, **kwargs)
+
+            send_func = run_sync(_send_multipart)
+        elif stream is not None:
+            send_func = stream.send_multipart
 
         if isinstance(msg_or_type, (Message, dict)):
             # We got a Message or message dict, not a msg_type so don't
@@ -856,11 +863,11 @@ def send(
 
         if stream and buffers and track and not copy:
             # only really track when we are doing zero-copy buffers
-            tracker = stream.send_multipart(to_send, copy=False, track=True)
+            tracker = send_func(to_send, copy=False, track=True)
         elif stream:
             # use dummy tracker, which will be done immediately
             tracker = DONE
-            stream.send_multipart(to_send, copy=copy)
+            send_func(to_send, copy=copy)
         else:
             tracker = DONE
 
@@ -907,8 +914,15 @@ def send_raw(
         to_send.append(self.sign(msg_list[0:4]))
         to_send.extend(msg_list)
         if isinstance(stream, zmq.asyncio.Socket):
-            stream = zmq.Socket.shadow(stream.underlying)
-        stream.send_multipart(to_send, flags, copy=copy)
+            assert stream is not None
+
+            async def _send_multipart(*args: t.Any, **kwargs: t.Any) -> None:
+                await stream.send_multipart(*args, **kwargs)
+
+            send_func = run_sync(_send_multipart)
+        else:
+            send_func = stream.send_multipart
+        send_func(to_send, flags, copy=copy)
 
     def recv(
         self,
@@ -932,11 +946,18 @@ def recv(
         """
         if isinstance(socket, ZMQStream):  # type:ignore[unreachable]
             socket = socket.socket  # type:ignore[unreachable]
+
         if isinstance(socket, zmq.asyncio.Socket):
-            socket = zmq.Socket.shadow(socket.underlying)
+
+            async def _recv_multipart(*args: t.Any, **kwargs: t.Any) -> t.Any:
+                return await socket.recv_multipart(*args, **kwargs)
+
+            recv_func = run_sync(_recv_multipart)
+        else:
+            recv_func = socket.recv_multipart
 
         try:
-            msg_list = socket.recv_multipart(mode, copy=copy)
+            msg_list = recv_func(mode, copy=copy)
         except zmq.ZMQError as e:
             if e.errno == zmq.EAGAIN:
                 # We can convert EAGAIN to None as we know in this case