That’s not possible if the steering shaft still has a master spline. The wheel only goes on one way if the master spline is present and unaltered. If you just clocked the wheel differently on the splines your master spline has been filed off.
If your steering wheel is that loose, the splines are damaged or worn out either on the steering shaft or the steering wheel/adapter. It should require a puller. If you can wiggle it loose, something is wrong.
If you’re careful enough to adjust the tie rods the same amount on each side there will be no issue with the alignment. You just have to make one side longer and the other shorter by the same amount. You can literally check the toe with a tape measure if you’re careful.