Jim -
Whatever tippet material I am using, when I tie a clinch knot, after I pass the tippet through a tip ring or through the eye of a hook, I form a fairly large loop and then hold the loop, with my left thumb and forefinger, wide open away from the tip ring or hook eye. After doing four turns using the right hand to complete the turns by passing the tag end over and around the standing tippet four times, I pass the tag end through the loop I am holding open and start snugging it up, after wetting it.
It seems to me that using this approach to forming a clinch knot would work with a swivel ( that swivels ) because you are holding the open loop firm and not even involving the swivel until you have mostly completed snugging the knot down. At that point, there is no reason for the swivel to swivel as you complete setting the knot.
John
The fish are always right.