If you trap them you have to prevent those lovely cuddly otters from becoming victims.
but once otters arrive you will know exactly how many fish are present in the lake, ,, they will be on the bank and easier to count. all dead and dying often with just a mouthfull of flesh missing, normally from the gill area.
you could of course pay large amounts of money to otter/mink proof the place, not always possible dependant on resources and location.
I have never known mink to destroy a fishery, otters on the other hand, 100k of un-replaceable specimen fish in a matter of weeks. in addition to anything else edible, frogs, birds including full grown wild fowl even geese and swans aren't safe.
if you notice ducks no longer flighting in even when food is supplied, you can take it as a given you have otters.
good luck.