Maybe, I remember there are a couple of products that you can either mount at the backplate or even inside the control cavity. There is something ILICH Electronics, but you definitely need to call them, they will ask you some specs or measurements from your pickups. I know cause once I called to potentially get one for MIM Ceramic pickups which sound great imho, but I never got to buy the coil from them.
If you just put the STK-S6 in the neck a couple of positions in the pickup selector switch will become noiseless, I get it, but is that really a bad thing? Do you use that much gain in the notch positions? I don't, just clean or mild overdrive that I can control with a noise gate then when when I crank the volume knob I always switch into neck or bridge which is already noise cancelling.