Storable can't serialize sockets, and all of the Perl shared memory solutions use Storable. You could try doing it in C instead, and linking that in using XS. Otherwise, I think it's impossible.
Comment on Re: Storing Socket Connections in Shared Memory
Not even C can't serialze sockets, at least not in user space and not to shared memory. Though some Unix systems (those that support STREAMS -- probably most non-BSD-based ones) will let you tell the operating system to stream an open file descriptor over a socket or pipe using ioctl() with the I_SENDFD and I_RECVFD.