If you want to maintain strength/muscle maintain intensity/volume as best you can, while cutting slow.That stimulus for growth is the same stimulus to hold onto lean mass while cutting down.
“Keep running whatever program you are on” usually works but in reality small modifications have to be made to be sustainable while cutting weight and adding in conditioning. Volume required to maintain gains is less than the volume required to make them so you have some wiggle room.
Gradually add in conditioning and progress it. The kind of conditioning will be determined by the sport. The more specific e.g. energy systems, movement patterns etc. a form of conditioning is to a sport i.e. scholastic/collegiate wrestling the better carryover in performance you’ll get. A wrestling coach would be handy.
Google “collegiate wrestling resistance training” and you’ll get loads of good stuff
If you’re conditioning really is terrible (thought strongman needed conditioning?) something non specific is fine to build work capacity e.g. stationary cycling or rowing machine for an hour at moderate intensity. As soon as you feel you are fit enough and have the required work capacity transition into more specific forms of conditioning.