Lookit, couple points:
1. If you have/use a "throwdown wallet" for a mugging scenario, then it would not be a very smart idea to *ACTUALLY* throw it down on the ground; that could really hack off your thug, and cause him to shoot you. You're much better off either (a) just handing over the throwdown wallet; then his mind is put at ease, thinking you are cooperating. He'll either turn and go, or look in it for money. If he looks in it for money, this should be just enough distraction for you to draw. If he leaves, so much the better - you're safe and you're only out a wallet, not several months of your life and thousands in attorney's fees potentially for having to shoot someone. Or, (b) tossing the wallet up in the air towards his face, so that he must flinch/deflect/catch - this ought to definitely give you enough time to draw. But simply throwing it down seems like a bad idea.
2. The techniques mentioned above, if aimed to allow you to distract him enough to draw and shoot yourself, can just as easily be done with your ACTUAL wallet, and no need for a throwdown. Unless you want to guard against the scenario where the attacker leaves without violence, being satisfied with your mere handing him of the wallet, by putting a couple/few dollars into the throwdown, and keeping your credit cards, IDs, & more cash in the real wallet.
3. As far as just drawing your gun instead of pulling out the wallet to begin with, this may or may not work, depending on the experience/sophistication of the crook, and more importantly, your gun's location. If you carry at the 3 or 4 oclock strong side belt position, then it'd be pretty easy, because it will look like you're going for your wallet in your rear pants pocket. If, OTOH, you have your gun carried in a SmartCarry holster, as I do right now, then reaching into the front of your pants is NOT going to look like you're complying and getting the wallet - you might just set him off and get shot. So in the case of smartcarry, if someone got the drop on me, I would first grab my wallet and hand it over, then look for an opportunity to draw. Most likely, I would try the "toss-the-wallet-towards-his-face" routine. While he's dodging/deflecting, I step quickly to one side and back while drawing.
4. If the thug takes complete control, and gets your wallet out himself, while you have to hold your hands up, then you're pretty much screwed over, unless you're fast & trained in jujitsu or similar techniques to quickly grab or deflect his gun and then grapple hand to hand.