Thanks for the full specs on the fans. I'm going to offer some different advice.
You do have two different fan types there, all by Cooler Master. Fortunately, they have set all of them up with separate wiring for LED lights and fan control, so each can be addressed separately. On each fan there is one cable ending in a connector with 4 holes in a line for the LED light power and control. CoolerMaster says these are designed to be compatible with several emerging "standard" connectors for LED systems, including some built into mobos by several makers, and CoolerMaster's own LED controller. So I am very hopeful that yours can be connected to the Silverstone LED Hub you got. However, there IS an issue there. The Hub's manual says it has some non-standard connectors on it which conforms with the difficulty you report. The Hub also says it comes with two splitter / adapter units that can plug into their hub's ports and give you a slightly different connector pair that DO work with other makers' LED light strips. So, first thing to check: do you actually have those adapter / splitter items with your Hub, and can you plug the LED leads for one of your fans into the output arm of those adapters? If yes, then MOST of that problem is addressed. What is missing is that you would have six such fans, but the adapters only provide 4 output arms. MAYBE you can get one or two more adapters like that from Silverstone?
Doing that will put all of the LED systems in those six fans under a single control. With the Silverstone Hub you have two choices - use the manual control box that comes with the Hub, or connect its control input socket to an LED control header on your mobo if it has one.
Now, control of fan speeds is a separate issue. It does involve a complication that has a solution. You are correct about their different designs - the 120mm fans all are of the 4-pin type, and the 200 mm ones are 3-pin type. Now, 3-pin fans can be controlled only by using Voltage Control Mode. 4-pin fans are best controlled by the newer PWM Mode, but CAN be controlled by Voltage Control also. To connect six fans together will require use of a fan HUB, which draws its fan motor power from the PSU, because no mobo fan header can supply sufficient amperage for those six fans on a single header. The dilemma here is that almost all fan HUBS are only for 4-pin fans and cannot control 3-pin units. The solution is one particular Hub, the Phanteks PWM Hub. It is different because it uses the PWM signal from a single mobo SYS_FAN or CHA_FAN header that really does use PWM Mode (needs to be set in BIOS Setup, often) to create internally its own group of six 3-pin fan headers that use the older Voltage Control Mode, which CAN control both fan types. So, you can use this Hub to power and control any mix of 3- and 4-pin fans, such as you have. It even comes with a solution to a small issue. The ports of this Hub are narrow enough that you often cannot plug a 4-pin fan into them. BUT the Hub comes with two of its own 3-pin fan splitters. For each you can plug it into a Hub port, and you get two 3-pin output connectors OUTSIDE the Hub case and free of interference, so you CAN plug your 4-pin fans into these Splitters.
So, OP, you can use the Silverstone Hub you have for control of the LED portions of all your fans, if you can get another adapter to enable connecting them all to the Hub's ports. Then you should get a Phanteks PWM Hub and use it (and its included Splitters) to connect all your six fans' motors together. This will put all of them under identical control of one mobo SYS_FAN header. I am presuming that all of these fans are to be used for case ventilation, and that cooling of the CPU chip is to be done with other means we have not discussed at all.
To be sure this can work, post back here the maker and exact model number of your mobo. With its manual we can advise whether you have a mobo port to control the Silverstone LED Hub, and how to connect the Phanteks fan Hub to the mobo.