Honestly, I don't worry that much about the unhappiness factor of using the whip. IIRC, the way the unhappy face is applied, it shouldn't matter that much anyway, even at the higher difficulty levels. In fact, difficulty level shouldn't matter at all (actually, should be less of a factor at higher levels). You're losing a pop anyway. And odds are it's an unhappy pop. You're just replacing one unhappy face for another.
Say you've got a size 4 city at deity level. By default, you've got 1 content and 3 unhappy ones. You've got one military garrison and two happy faces via luxuries/entertainment. This results in 2 happy citizens and 2 unhappy citizens. You're at your limit really unless you add more happy effects from somewhere.
You rush a build at the cost of one pop. You gain an additional unhappy face (how long do those last anyway? Not long IIRC). So now, you've got three citizens and all three are unhappy by default (cause of the extra unhappy face). You then apply your garrison and luxuries and you end up with one happy, one content, and one unhappy citizen. The city is just as productive as it was before. Hopefully, the extra unhappy face will go away before your city grows back to size 4. If that's the case, it didn't actually cost you a darn thing to rush the builld.
At higher levels, early in the game, you just can't manage larger cities. You don't have the luxuries or units to garrison. Killing off the pop (ok, for the PC crowd, they're "leaving"... Yeah... Right

) is something you want to do. Remember that if you have to build an entertainer to keep your city from going into disorder, you may as well have used that pop to rush a build instead. While there's more strategy to micromanaging your specialists then I care to get into right now, as a general rule, a worked square is better then a specialist. In most cases, a built unit/improvement is of more value then a specialist as well.
My general rule when in despotism early in the game is to rush build everything as fast as possible. The first turn that you can rush with a cost of only one citizen is the turn you want to rush it (sometimes I'll even do it at a cost of two if the city's growing fast ). You have very few advantages against the AI early in a high level game. Effective use of rush building is one of them. Learn to use it correctly (as well as worker and settler farms), and you'll be able to hold your own against the AI's ludicrously high production rate.