Moving on a bicycle is all about Power. If you put with your feet 10Watts on your superlight, aerodynamic recumbent, you won't go fast. If you have 800Watt available on your grandma's  bicycle, you will pass lots of fast cyclists.
We can imagine ourselves a lot of interesting power sources. Today the electric battery is widely available and motors are fair good enough to mount on any trike or bike. After some years of troubble with BionX, we work now with Crystalyte. Good price, good quality, no nonsense way of working.

The system we install most weighs about 9,5kg, included a battery of 9Ah. That means your hybrid bike weighs apparently more than your naked bike. If you want to ride a certain moment without the electrical assist, you will have to push harder.
The question poses now; are you happy with the effort you do on your naked bike or not? If you are not, install a motor; he will help you to attain a certain speed with much less effort. Or he will attain a speed you would not keep for a long time on your own. And you don't loose the benefits for your healt because you have to keep pedalling.

Note that you will drive our Waw allready pretty fast with you own power. Maybe you have to try first without motor, it can be installed afterwards.