A full 6" of cat whisker silencer weighs a whopping 38 grains. By the time you tie it on, trim it back...you might add 20-25 grains to the string (10-12.5 grains in two different spots)--I cut half or more of mine off when I trim them back. You'll generally add that much or more building up the center serving on a skinny string (extra strands, double serving), and to a point on the string that is much more critical.
The 4 extra strands in the 12 strand string will weigh about the same as the cat whiskers, or a little more. Can you weigh the two strings to compare?
Based on that (I just weighed all this on my grain scale), there's no way the silencers are the culprit. Even without silencers on the 8 strand, it's not going to make anywhere near a 10" difference in your point of impact (assuming you were aiming at the center of the target) at 15 yds--maybe at 100 yds, but not enough to notice at 15.
I've swapped around with several differnt types and diameters of strings on my personal longbow--from 12 strands of 8190 (TINY string--about the same as 8 strands of 8125, or 6 strands of Dynaflight '97) up to 14 strands of Dynaflight '97. I don't have to swap arrows, point weight, etc.--it shoots just fine (according to my tournament scores at least).
Very few people shoot accurately enough to shoot the difference in strings that differ by a few strands. There might be a very sensitive bow here and there that shows the difference more than others...but that bow will be sensitive to most anything...arrow spine, release, silencer placement, etc.
'Course if you have decided in the back of your mind there's going to be a big difference before you release the first arrow, then you'll probably see a big difference regardless.