Let's back up a second and define what "External Hand Razors (non-ware)" are. Because I'm only aware of hand razors being implants.
Hand razors are like sharp fingernails, about an inch long. In 5E, all cyber melee weapons use Unarmed Combat (page 458), potentially with the Cyber-Implant Weapons specialization. If there's a non-ware version then I haven't heard of it and I'd ask for a page reference to see what I missed.
Forearm snap blades are the non-ware (external) equivalent of cyber spurs. Per page 422, these use the Blades skill.
So which weapon are we talking about?
In 4E, cyber-blades in the hands or forearms used the Blades skill, while other implant weapons (like shock hands, or blades in other places) used Unarmed Combat. So there's certainly precedent to use Blades in addition to or instead of Unarmed Combat.