Pass the `net.Conn` object when creating the client instead of passing it to the
`Handle()` method that keep a reference to it. By doing this we do not
have to worry about read or write race over the internal field. The
client still need a reference to the connection when the out of bound
call to `Close()` is executed to make sure we are getting out of a
`Read()` call early.

Tested with :

```
while true; do go test -v -race; done
```

Found in elastic#13021