It feels weird in both hands when you start - but weirder in your non-dominant hand.

Although it is fine to use just your dominant hand, a lot of us do use both.

Take your time, don't rush things - maybe just do the cheeks first time, stop and introduce other sections as you get more comfortable.

Take your time - don't need to do it all the first time. Get used to the blade.

You can practice sitting around with the razor, just getting used to holding it in both hands (if that doesn't alarm any family members).

Dry run with butter knife - can try working out strokes / passes with a butter knife before actually using the razor.

With practice, your hands do get used to using the razor - and did I say take your time?

Just a few thoughts.
Enjoy the journey,
Michael.