What you suggest may work. Certainly I recommend you disconnect the case-supplied Hub and connect the speed signal cable from the PUMP unit of the H199i system to your CPU_FAN header.
How to connect the four fans supplied with the case is a bit different. The case web page says it includes four NZXT FN V2 fans, which are 3-pin design and require Voltage Control Mode (aka DC Mode) to control their speed. The Hub you have does that on all outputs except the white Port #1, so at first glance that seems good. Now, to do that, you would plug its input cable into one of the CHA_FAN headers on your mobo and make a few configuration settings (see below), then plug your four fans into Hub ports OTHER THAN Port #1. (If you plug one of those fans into Port #1, it can only run full speed all the time.) However, the problem becomes that the Hub reports back to the mobo header the speed of the fan on Port #1 only. If there is no fan there, the mobo header will detect no fan and may issue constant warnings that the fan on that header has FAILED. There should be a way to deal with that in header configuration.
So, if you proceed that way, here are configuration details. If you don;t yet have it, download your mobo's BIOS manual called PRIME TUF GAMING B550 Series BIOS EM WEB EN from its website here
https://dlcdnets.asus.com/pub/ASUS/misc/Manual/PRIME_TUF_GAMING_B550_Series_BIOS_EM_WEB_EN.pdf
Start on p.5. To get into BIOS Setup you must press the "Del" key immediately after starting up. I always Press and HOLD that key to be sure the system "sees" your action, until the opening screen of Setup appears (manual p.6). Look at bottom right, and press F7 to get to Advanced Mode (p.7). At the top click on Monitor to get to the Monitor Menu (p.37). Clock on the particular Chassis Fan header you want to configure, and then see p. 39 for details. Set options as:
Q-Fan Control to PWM Mode so the Hub receives the PWM signal it needs
Chassis Fan Source to Motherboard so it uses that temp sensor
Chassis Fan Speed Low Limit to Ignore so it does NOT worry about no speed signal coming back from the Hub
Chassis Fan Profile to Standard to use the automatic default fan speed control plan based on temperature at the selected sensor
When you have those set, use Esc to get back to the Monitor Menu. There click on Exit at upper right to reach the Exit Menu (p. 49). Choose Save Changes and Reset to save your new settings and reboot.
This should allow you to use the Hub you have to power and control the speed of all four of the 3-pin case ventilation fans you have, based on the temperature sensor on the mobo. The mobo should NOT give you any hassle about not having a fan working on the CHA_FANn header that the Hub is plugged into. However, with this arrangement, that header can NOT monitor the speed of ANY of those case fans for possible failure. So from time to time, YOU should just check that they all are working.
Meanwhile, your H100i system will manage cooling of the CPU, with its pump speed reported properly to the CPU_FAN header. A small note: you can rely on the speed and temperature info shown to you in the Corsair iCUE utility. IF you use BIOS Setup to look for the speed of your CPU cooling system, it will label the speed it has on the CPU_FAN header as the FAN speed, because it does not know that you really have a PUMP connected there. Do not worry about that.