As the wire is thin any IR transmission gap sensor would liekly need to be sensitive with an analogue output, to detect a drop in intensity as the wire crosses rather than a total blocking. Whether reflective IR could work will depend on how shiny the wire's surface finish is.
You want to avoid any sensor that could cause a complete circuit, does that mean a current is running in that wire between the drone and somewhere else, or that the wire is held at a particular voltage? Either of those possibilities would open up more sensing possibilities, Hall sensor ifa current is flowing for example.