In an arcmap solution, I would first move all features to a geodabase. This would automatically add geographic fields such as length, area of features.
I assume that the waterways are a polygon feature and not line features since there are lakes in it.
I would union the county and water feature to slice up the former layer with the features in the latter and adds attributes of both. Benefit is you have a full layer, including waterways, but they are segmented into water and not water features for later analysis.
Then you can select water features in the new county layer and either delete them or definition query around them.
You can then do your summary of the county area, sans waterways.