Since this is the closest I could think to be the appropriate category, how about basically what this whole section is about for men? Vegan skincare and grooming products for men are kind of underrepresented.
LA Shaving Soap is entirely vegan and all their soaps are fantastic.
Ursa Major does more standard skincare products, like face wash and moisturizers. By far the best I've used, though they definitely run pricier than many others.
What do you use?!