From the point-of-view of a hive swap, bees fall into two categories: young bees and older bees.
Young bees haven't been out flying yet, and so will stay wherever you put them. Older bees, on the other hand, have been out flying and have thus oriented to a hive entrance location - which, having done this, means that they will auto-locate towards that location - even if it looks different.
So - simply place your new hive in the old position, with it's entrance as near as possible to the position of the old entrance, and facing in the same direction. This isn't critical, but the nearer it is to the original, the better,
Place the old hive as far away as you like - a few yards is fine. Then move your bees. Any residual bees (there's always some) can be scooped-up using a brush and a scoop made from a plastic milk jug. Then, just tip 'em in.
When the foragers return, they'll simply enter the new hive - there may be a little hesitency at first, but they'll soon adjust. It's usual to get some clustering around the entrance for a couple of hours, as they become aware that 'something here isn't quite right' - but again, they'll soon adjust to their new home.
If any bees do choose to fly over to the old hive, then providing the entrance to it is blocked, they'll soon figure out where the rest of the girls are now living.