Welcome to the forum. You should be able to left-click on the Part and move it. That won't affect any other components unless they're linked to it with Mates.
I have tried that, but I am unable to move that part without moving the entire assembly with it. I have deleted every mate on that part (Which is in a sub assembly) But everything in that sub-assembly still moves with it. It is also in float mode.
You can also right-click the part and select move with triad.
Also, you can suspend your mates and then modify them for the new location (if reusable) while they're still suspended.
Then unsuspend the mates when they're repaired.
This way you can avoid SW complaining about busted mates and potentially you don't have to recreate as many mates.