A watch that tells the time, but doesn’t have a face? That would make it impossible, and very confusing. However, there is such an object; heck, I thought it was just a bracelet. Using LED lights to show the time in the traditional digit format, it will show the time (in 24-hour time) with a press of a button.
However, the store is from Japan – and ordering it online is for “domestic customers”. Also, sadly, it isn’t on sale – just only saying it is “Coming Soon”.