Your answer is at the end of your post - ONLY way is to use the hand-held manual remote control supplied. Note that the case includes a fan control board (controlled by the remote box) that controls BOTH ARGB lights AND fan speeds. On common fans, those two functions are fed and controlled separately using TWO cables to each fan with "standard" connectors and wiring schemes. IF your fans are made that way, it is possible to NOT use the case's board and connect all your fans' cables to mobo headers. BUT your fans may not be that way - many case makers that include all that stuff have non-standard single cables from each fan with six-pin connectors that cannot be plugged into a mobo header.
Even if you have fans with separate and standard connectors, you still do NOT have a mobo ARGB header to plug into. So your option (other that what you have) would be to buy another third-party ARGB lighting Controller that comes with a software utility to allow keyboard control. Then you also might be considering connecting the fan MOTORS to your mobo fan headers. It's all possible MAYBE, but using what you have is simpler.