In your situation I would remove the pusher electric fan. More than likely that fan doesn’t push enough air (CFM) to be a standalone fan.
With the electric fan removed you can then see where you’re at with the mechanical fan, but based on what you’ve said already you should add a fan shroud. You should also measure your fan and crank pulley diameters to make sure you’ve got a pulley ratio that’s correct for your application. What water pump are you running?
I’m all for electric fans, but running a stand alone electric fan on the street is a lot more involved than just taking the mechanical fan off and slapping an electric fan on. The fan has to be able to flow enough CFM, which typically requires a higher output alternator and a heavy duty relay system. It also needs a good controller for street use, which usually needs its own sending unit, etc. A strip only car can get away with a simple on/off, but that’s not how you want to run on a street car. So unless you’ve already set some of that up, it would be easier to just remove the pusher and figure out what your cooling system needs to run efficiently (shroud, proper pulley ratio, etc)