I can't think of a sentence in which we can use however and on the other hand together, except with a different meaning for however from the one you are thinking of:
On the one hand, Fred was very careful with his money; on the other hand, however mean he appeared, he never accepted anything to which he wasn't fully entitled.
Fred was careful with his money but, although he appeared mean, he never accepted anything to which he wasn't fully entitled.
Fred was careful with his money, and made no secret of this; in contrast, Bill, while appearing generous on the surface, was actually very mean and grasping.
You will notice that I have not used any of your pairs in the same clause.
Student or Learner