This is kind of like, "Doc, it hurts when I do this!" Doc - "Don't do that!"
But seriously, a hangover is a low-energy state and depression is a low-energy state. If you do anything that produces a low-energy state, you're going to be depressed. Ever seen anyone with a high-energy state and feeling good that was depressed? Won't happen. Or if you know a way, please let me know.
That's the bad news. The good news is that if you stick closer to pure likkers like 100% blue agave tequila and most (but not all) straight bourbons (with no gluten), you're much less likely to have a hangover, provided, of course, that you are still capable of a certain amount of restraint and wisdom in your drunken stupor. Nothing will depress you quicker than sweet, sugary alcoholic drinks, rum, beer, and the sweeter wines. Those are for kids anyway. Real men and women have learned to get away from that stuff and stick to good likker.