Match the method to the pest
Tank pests covers very different animals — planaria and hydra, pest snails, hitchhikers on new plants, fish lice and anchor worms on the fish themselves — and the safe response differs for each. Before anything else, get the pest identified: what flattens your shrimp-safe options is that shrimp and snails share the invertebrates' sensitivity to many of the chemicals used against pests, so a treatment chosen for the wrong pest can be both useless and the most dangerous thing in the tank.
Physical removal: the always-safe first line
Nothing you remove by hand can poison anything. Siphon visible worms and pests off the glass and substrate during water changes, scrape and net out what you can see, and use a baited glass trap for planaria, lifted out each morning with its catch inside. For pests on individual fish, such as lice, the fish can be caught and the parasite removed or dealt with in a separate hospital tank, leaving the main tank's invertebrates untouched by any chemical at all. Pest snail numbers respond to a blanched vegetable leaf left overnight and removed, snails and all, in the morning.
Starve the population down
Most pest outbreaks in a shrimp tank are feeding outbreaks. Planaria, hydra, and pest snails all multiply on leftover food, so feed in a glass dish, remove what is uneaten within the hour, and vacuum the substrate where fine food settles. A population that stops growing is often a population you can live with or trap out gradually — and in a breeding shrimp colony, slow and safe beats fast and chemical as a rule.
The copper rule and label reading
The ingredient that makes so many aquarium treatments lethal to invertebrates is copper, present in many parasite and snail treatments. Read the full label of anything you consider, not just the front: look for explicit wording that it is safe for shrimp and snails, and treat silence on invertebrates as a no. The same caution applies to some plant fertilisers and algae treatments that carry copper in small print. If a treatment is genuinely needed and its safety is uncertain, move the shrimp and snails to a plain holding tank with their own water, plants, and a seeded sponge filter first — carbon in the filter and large water changes afterwards clear residues before they come home, and some keepers never return treated substrate or wood to a shrimp tank at all.
When to escalate
Pests that are killing fish, or an infestation that physical methods and feeding control do not dent after a couple of weeks, justify outside advice: take photographs and a description of your stocking to an aquatic shop or vet, and be explicit that the tank holds shrimp and snails, because that single fact changes every recommendation. Before pouring anything in, put a follow-up question to KinsLe's Kinny; he answers using the KinsLe Answers library.