It's not the handling that will be affected. The handling is the way the vehicle responds to dynamic inputs from steering, braking and power application when compared to what is expected or desired.
A 'hybrid' will involve a lot of engineering issues probably more concerned with the road-holding on different surfaces. You could build a hybrid which would be stunning down a drag strip where power-to-weight ratio and the transmission of the power to the ground are the critical factors. But ask that car to go around a corner, especially if it is a bumpy road, and it's entirely different.
Then again, it might be possible to get really good road-holding on dry tarmac with a hybrid, but the handling might be dreadful.
It comes down to how good a vehicle dynamics engineer you are. Doing the installation is relatively easy, it's making it all work in an acceptable way. I would bet that my Mk.1 Cooper 'S' with its 1310 cc engine giving c.115 bhp would be quicker than almost any hybrid along a bumpy & twisty road, but that I could be 'blown away' in a straight line on smooth tarmac.
The question might be why would someone take a valuable classic car and make it a less valuable hybrid with performance which is hard to use on a public road. Maybe it's the simply engineering challenge, as it's not cheap to do and for the same money a really quick modern car can be bought.