I am not 100% familiar with real life CC OPS, but I can give a common sense ATC answer. Using TNT/DAYNE traffic as an example. Once Trent sector has transferred the traffic to you, you must cancel the hold. Then you can vector it how you like. In LC you would have to avoid traffic that is not highlighted to you. I don’t know when the transfer normally is, have not run CC INT in years, so it might be well after TNT.
In real life the TRENT and CCINT would coordinate if a shortcut is used. CCINT can request traffic on a specific heading and level from TNT to avoid traffic routing all the way to DAYNE. Once transferred and within their airspace, they can vector it. In quiet traffic lots of things can be done with shortcuts and higher/lower levels than standard, but coordination is still required.
In LC this is tricky to mimic. As all traffic needs to have a ‘Hold at [fix] assigned and cancelled. Otherwise it messes with the subsequent traffic.
Hope this helps, C