Maybe this has no basis in reality, but one reason I stopped cycling as a primary form of cardio ( I run now ) is I just felt wrong moving from sitting at a computer to sitting on a bike.
So don't sit on your saddle—take it off. (Bonus reason: saddles {with a nose} also cause erectile dysfunction; I don't have any sources at hand but I'm sure if you search you will find).
It appears you're onto something with the erectile dysfunction. Apparently however, it's not that common and you can get seats that minimise the issue.