I don't know how big your tank is, but there are many fish that could live with your knife and eat all the snails. I have a ton of malaysian trumpet snails in many of my tanks and they are the cleanest tanks I have. The snails clean up the fish waste and aerate the substrate from constantly turning it over. I personally like that there is more life in my tank then just fish.
When you say a "big" clown knife what do you mean. To some a 12 inch is big, I just lost a 20"+ royal and I have seen others much larger than mine. Point is there are lots of fish that can go with the knife which can limit the population. If you kill them all off you will have an ammonia spike that could cause issues. Most omnivorous cichlids, motoro stingrays, any freshwater puffer, and of course large clown loaches would all work in your tank. If you have a knife that can take down a 7 inch clown loach you need to post pictures of him.
My advice, if you really can't stand them then trap them and remove them. Killing them in the tank will only cause massive problems. I would leave them if I were you and slow down on the feeding of the clown knife, he may try escargot if he gets hungry enough.