First, don't be afraid to just try the move and see what happens. You can always UNDO
If you use the command under the EDIT menu called "Circuit Move and Copy" it will definitely work,
but I always have trouble with it placing the group off-grid, and for some reason I still like grids
(old guy alert) There is a way to set the snap point but I can never figure it out
The EASY option to do what you want to do is to select the traces that you want to keep in that area,
and then click the "semi-fix" button, between the "Fix " and "Un-fix" buttons on the routing toolbar,
then go into the place mode and move the group. The traces should stay they way you created them.
and again, don't be afraid to try both ways and UNDO whatever you don't like...
Jack