Pond snails like all creatures have to conform to population restriction factors which the main one for "pest" snails exploding in population being food supply. If you feed your fish less or have less food then your population of snails will not be able to grow as rapidly or to such a size. Assassin snails will eat pond snails but they don't feed very regularly so I would not consider them an effective solution nor should you in my opinion add a species to your tank which you do not want simply for their own beauty/character. If the Assassins eat your entire population of pond snails you will then have to feed them independently which adds a chore for an animal you have been enticed to purchase to alleviate the issues of another. I love snails I added ramshorns, pond, apple, assassin, malaysian trumpet and nerites to my tanks as they fill a biological niche and I find them fascinating like the other inverts I have.
Assassins will not eat shrimp unless the shrimp is dead already and there is a weak fresh molt or a hole in the exoskeleton
To get rid of pest snails takes time:
Pick out (do not squish as this can cause them to release eggs) as many as you can possibly see and attempt to scrape the eggs off the glass of the tank regularly. Blackout the tank for a week (restricts algae growth thus food supply) and during this time do not feed your fish at all independently (if they nibble at the snail traps that's fine), place a couple (depending on size of tank) of slices of courgette in the tank (weighted down) and allow the snails to be attracted and start feasting then remove (takes 2-4 hours to catch a good amount normally). I do not recommend placing the courgette in over night as your going to feed at least half the population before you actually remove it. If one period of this doesn't eradicate them have 3-4 days of normality and continue with a 2nd week.
