You dont have to fertilise in a wet area to have a good lawn rain does
that, fertilise and it will grow twice as fast. I rarely fertilise , I
did not last year and I had to cut only every month in heavy shade. I
have fertilised and made it grow where it needed 6 cuttings in a month.
Don`t fertilise if you must till after a few cuttings, I would not use
weed killer till its needed , let the lawn get strong .