Small amount of water in chimney after rain
As long as your chimney cap (I assume that's what you describe as a 'cowl'?) is in place, you are probably fine.

Although chimney caps are designed to keep out rain and critters, they can't fight the occasional sideways rain drop. The little amount of water that enters the chimney from those atmospheric anomalies won't hurt a thing. Short of completely blocking off the chimney with a weathertight cap (not possible if you use it with gas appliances, as you stated), just keep truckin.