I vote for the liquid nails/JB Weld sort of thing... here is why. Is this actually providing holding power, securing the fly sparge contraption?
#1. It never contacts your wort.
#2. The cooler lid is probably HDPE, and silicone will not bond to that smooth surface very well
#. Silicone is not very robust, not a lot of HOLDING power, great for sealing though.
I vote for liquid nails/JB Weld... I have done a lot of building
Also, from your other thread, if you are going to fly sparge, you need to ditch the braid.