Try connection draining. It will send all new requests to the environment you want while giving time the other to fall off.
a max-lifetime of your web socket can be set and always remember to keep the connection draining period longer than that of your web socket.
Or you can just handle the client side. If at any time web socket connection stops you can start a new one through AWS ELB to an active server. This should work even when you're scaling down on AWS. Also remeber not to keep any state of your ephemeral ELB backends.