Yes, you can remove the forks and wheel together as a unit but this will make it significantly harder to do, especially single-handedly. This way would require that you raise the front end quite a bit higher than if you removed the wheel first. Some people raise the front end by suspending it from an overhead beam. If you only have one lift, you might want to "borrow" a milk crate from your local supermarket. A metal one would be best, but plastic will work also. You may need a few spare boards to raise the front wheel enough to remove the wheel.
Assuming that you are satisfied with the way that the donor bike rides, here is what I would suggest to maintain that alignment when the forks are transplanted onto the recipient bike. Take a Sharpie and make a mark on the fork caps that matches the pinch bolt slot on the upper triple clamp. This way you can line up the legs in the same orientation as they came off. Once the upper and lower pinch bolts are loosened, grab the upper fork legs and see if they can be twisted down through the triple clamps. If they will not rotate freely by hand, take a large flat bladed screwdriver and insert it in the pinch bolt slots, and carefully pry the slots open just a very small amount while twisting the upper fork legs. Once they are freed up, you should be able rotate them down through the triple clamps.
For re-installation, just reverse the above procedure.