^I've seen that recabled RE-600. You're not going to get a "factory look". I hate to say it, but getting a recabled factory look is next to impossible unless you use the same RE-600 cable. The RE-600 cable was made specifically for it and no other iem on the market that I know of uses it. The benefits of recabling it yields long term durability. Most cable failures don't occur within the cable, but with the cable soldered to the connector, or at the other end of the cable where the solder points on the drivers. I would first replace the 3.5mm TRRS connector with a much higher quality one and retain the original cable for that factory look. I've replaced the TRRS connector on a few RE-600 and the wires soldered to the stock connector is not that secure nor robust.
What I mean by factory is any factory looking cable, does not have to be by HIFIMAN. The cable can look like a Westone or Shure, a cable with a molded sealed jack and a molded split. I don't like these twisted open cables and nutrik huge plugs, looks very second hand and homely/nasty. For example, if someone could put a Weston 3 cable on the RE-600's that would look somewhat a factory type as the cable is by a manufacturer. That is what I mean, sorry I was not clear.