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Aperture affects both flash and ambient. Shutter speed only affects ambient (a simplification) because the flash duration is so short that all the light gets in whether shooting at 1/2 second, 1/20 sec., or 1/200 sec.
So, use the reading off your flash meter as a starting point, then get to the aperture you want by using equivalent exposures. If the aperture you want requires a shutter speed faster than your maximum sync speed you'll need to cut the amount of light by using using a lower ISO setting, using ND filters, dimming the lights, etc.
If it's hard to imagine why one affects both types of light and the other doesn't, here's a thought experiment:
Picture a fat guy and a skinny guy trying to get through a small manhole. The skinny guy (dim light) can get through easily. The fat guy, no matter how fast or slow he runs (shutter speed) can't get through. So speed doesn't change the outcome of door size (aperture).
Now picture a door (shutter) that opens and closes really briefly. A slow walking guy (ambient light) can't get completely through the door before it closes on him, but a fast runner (flash) can.