I don't know enough about shaving mugs to be able to date it precisely, but this unmarked heavy milk glass mug is definitely old and not a modern remake. I'm pretty sure post-1920s men did not prefer to have their shaving gear decorated with flowers. In addition, the glass is a little swirly and mottled, and more of a pale beige color than pure white. The mug is 3-1/2" high by 3-3/4" diameter at the rim. The front has a hand painted decoration of orange or faded red daisy type flowers with green leaves. There's a little fading to the painted design, not bad. No chips, flakes, or damage.
Milk Glass Shaving Mug Hand Painted Flowers