Yes, this is a no...unless you want to risk treating your snakehead for ich. No one can guarantee what will happen, but there's much more than a non-zero chance the snakehead will get ich if you do.
Also you should know that simply moving the net from one tank to the other, using the same buckets or cups, using the same hoses could transfer the parasite.
If it were me, I'd sterilize all the utensils and the feeder tank, sooner rather than later.