How to use capacitor as battery in razor?
so any help will be appreciated
  via AC Adaptor it's too weak, maybe because the lack of backup power
  like capacitor
  


For the sake of argument, say the battery was 4 volts and delivered 250 mA to the motor during the minute that you are shaving. That's 1 watt for 60 seconds or a total energy of 60 joules.

A 1 farad capacitor charged to 4 volts has an energy of \$\dfrac{CV^2}{2}\$ = 8 joules.

But it's a little more complex than that because you realistically don't want the voltage to deplete below 3 volts or you motor isn't going to turn and the equation above is for full depletion energy. So, you want to leave 4.5 joules left inside the capacitor to avoid dropping below 3 volts.

If you had a 20 farad capacitor charged to 4 volts, energy aka work or W = 160 joules and at 3 volts it's 90 joules so that would be about right for your application - 70 joules of energy is bigger than that energy needed to take a shave (60 joules by my reckoning).

The next trouble is finding a 20 farad, 4 volt capacitor. The nearest I could find is too low in voltage so, you'd need to have two in series of 40 farads each. Then you have the problem of balance charging super capacitors in series (not trivial): -



These cost £5.84 each in Farnell. Your choice.