If you ride a hybrid now without bike shorts and without pain, I think it is more about the saddle setup or the saddle itself.
As you bend over more to lower handlebars you are going to compress things. I have found that saddle tilt, and the right saddle, is pretty important on a road bike, at least for me. But too much downward nose tilt can put too much weight on wrists and shoulders.
Years ago, no one made cut-out saddles and few had channels. Brooks was, and still is for some, the saddle of choice to conform to your shape. Today saddles are designed to reduce perineal pain.
John