I don't think you'll need to go through the trouble of acquiring a syringe to use
kalk paste to kill aiptasia anemones.
Carefully mix the powder with a little fresh water in a small glass or plastic cup until it
gets to a semi-watery paste consistency.
Use a turkey baster to draw in some of the kalk paste, being sure to keep the open
end of the baster up, and then put the turkey baster over the aiptasia and cover it
with a layer of kalk paste. Be very careful to only use a small amount, and watch out
that none of the paste slides off the rock and lands on any organism - if you can get
the rock that has the aiptasia out of your tank, and use the kalk paste in a bucket all
the better.
I use kalk paste to trim a population of blue actinidiscus mushrooms that sometimes
get too close to some sps colonies. As long as small amounts are used, and you're
extremely careful - the paste is caustic with a ph of 12. Eye protection and gloves
are recommended.
I've never employed a peppermint shrimp to get rid of aiptasia.