When you left the cowl off was it in 2 parts so that the base still covers the top with just the 150mm SS inner pipe exposed? Mine was one piece and fixed with 2 x 8mm roofing screws into the outer flue.
Creosote from wood isn't nearly as strong as from coal and is used in smoked foods so not really something to worry too much about. Good point though, I have a rainwater tank and go to a lot of trouble to keep it as pristine as possible. If it hasn't rained for a couple of weeks in the summer I drain down all 3 systems feeding the tank because that's where the algae and bacteria breed from the light getting through the pipes above ground.
Here's the first cowl type on the left and the new type now fitted on left of the right hand pic.
A I mentioned before, the first one fits perfectly into the venturi, without needing screws for warm weather rain proofing.