Replacing 1.2v Ni-Cd battery with supercapacitor
Lets assume your trimmer draws 600 mA while running thereby giving you a backup of 1 hour on full charge.

Resistance of trimmer = 1.2/0.6 = 2 ohms

Now lets assume the power is being provided by a supercap. Lets further assume that your trimmer will work in the voltage range of 1.4 V to 1.1 V without any issues and you would need a backup of at least 20 minutes so that you can shave after one charge.

Refer to the discharge formula given below:


Vc = 1 V

Vo = 1.4 V

R = 2 ohms

t = 20 mins = 1200 seconds

Calculation gives C = 2000 F.

Yes, that's farads.

So, lets talk about feasibility. Here is a 2000 F capacitor from digikey:


This has a dia of 6 cm and height of 10 cm and costs 56 USD.

If this size and price point is okay with you, you can go ahead :)

Edit : Corrected capacitor specs.