While time-consuming, removing everything altogether and putting it back in the new location is the best way to move a server. Trying to take shortcuts will only risk bending your rails, making them unusable. (Bent rails are hard – if not impossible – to bend back.)
Never mind the possibility of dropping your server outright, possibly damaging yourself, the floor, or other servers!
This is also a good time to fix your cable management if it’s sloppy…
Also, since you should be taking an outage on the server (you are shutting it down, aren’t you?), it may be a good time to do those things that you don’t otherwise have time for, like firmware updates?