It's funny that I used to buy 'sensitive' shaving gel, and one day I thought what makes me think I have more than average sensitive skin? I then found out that soap works well enough.
"Ordinary" soap does work but I find it tends to dry out more quickly than I can shave my whole face hence at home I use shaving soap with a brush. But when I travel I'll happily use the hotel's free hand soap at tbe destination to save the hassle of bringing more things through the airport.
I always assumed that the sensitive skin isn’t on your face.
Soap is, indeed, “good enough”. But for a minimal investment you can buy the shaving soap cakes, cup, and a shaving brush. Way cheaper than the stuff in a can, a little more luxurious than hand soap.