When you use a flash, the shutter speed is not that important. Since the flash fires all its power in 1/1000th sec or less, it is not important whether your shutter speed is 1/200th second, or 1/100th, or 1/4 second. Only the ambient light will be affected; not the flash part.
Take this, from a Goldcorp goldmine I shot earlier this year in Timmins, Ontario:
3200 ISO, f/4, and 1/4 second. Handheld.
Why so long? Because I wanted the light at the end of the tunnel to look like, well, the light at the end of the tunnel. And I needed f/4 for depth of field, hence 3200 ISO and 1/4 second.
But Michael, things will be blurry!
Not if they are lit by the flash. 1/1000th sec is 1/1000th sec! And if they are also lit by a little ambient light, then a little ghosting will appear, mainly in the moving parts:
Use a wider lens, and go slow, even very slow, any time you are using flash and it’s mainly flash lighting the important bits!