I can't speak for Wukong specifically, but there are cases of "after cast delay". Or, if you're familiar with fighting game mechanics, it's essentially "recovery" time from executing the attack. Once the recovery period is up, then you're able to resume your assault - otherwise, you must wait.
There's two different forms of skill "recovery" that are implemented in League of Legends for some skills.
The one you're probably experiencing is simply that there is a short recovery period after the resolution of the skill where you cannot act. For example (and this may just be what you're experiencing), Nimbus Strike has a tiny delay between when you make contact with your staff and when you can start acting again. There's a short delay after Blitzcrank purges his Static Field before he can start moving, and Ezreal's Arcane Shift has a tiny delay after you arrive before you can use another skill or attack. The logic behind this is essentially an extension of the reason you can't use skills or attack in the middle of the action to begin with - you're still in the middle of using the other skill. It rate limits your ability to chain skills instantly together. Contrast something like Tristana's Rocket Jump, where you can use skills even in mid-air.
The other form is that some champions, namely Sona and Udyr, do have a forced cooldown on all of their skills after using any single one. In their case, this is to simply rate-limit their ability to cast their spells sequentially - no song spamming, and no ridiculous stance chains.
Sivir's Boomerang Blade can be an annoying harass, both at early level and late game. Unfortunately, it mostly takes practice to be able to avoid it. But there are a couple of tips that I think (hope) will be helpful in the long run.
Placement
Sivir's Boomerang Blade has a fairly large attack radius. Where you are in relation to where Sivir is when she launches the attack can make a fairly significant difference. The important thing to remember, though, is the further you are from her, the longer you have to react. Try to remain at a distance as much as possible when facing Sivir; especially in early game. One more important point on placement, the more minions between you and Sivir, the less damage you will receive if Boomerang Blade hits you. Each enemy it hits makes the damage to the next enemy lessen.
Movement
Unfortunately for you, sometimes dodging her initial attack ins't always enough. Her blade will track with her, if she moves up or down on the battlefield. You should always move in the opposite direction from Sivir. In the following image, consider your Champion to be X, while the colored arrows show the path of the blade upon return, in relation to Sivir's movement.
One last point worth mentioning is this: While the camera is zoomed in in that image, it's important to remember the high range of Boomerang Blade. It will extend to the far edge of the screenshot.
If you can't always avoid the first shot, pay close attention to avoiding the return strike. But in the end, it really comes down to practice, practice, practice.
Best Answer
I always look at the creep waves to determine when to harass. I like to think of the situation in terms of a decision where to put each of my auto-attacks when attacking at max speed or if I want to wait on my attacks to get the response time to 0.
If the enemy creeps are all at high health (not last-hitable) and I see that one of my friendly creeps is at low health then I know that the enemy will be looking to last hit so I take that opportunity to hit them with an auto attack. Basically, if I can hit them without losing a CS or putting myself in danger then I will do so.
The main key here is to watch the creep health bars and start considering your allied creeps health in order to know when the enemy will be trying to last hit. If you know that their auto-attack will be spent on a creep then you know that you can hit them once without taking damage yourself.