Genuine question but would there not be blood loss no matter how carefully the main blood vessels were left intact? Maybe that's just superficial all told, or would it need to be cauterised?
The query reminds me of something I read years ago where a 19th Century US soldier recalled an encounter with, I'm nearly certain, one of the Sioux leaders. Captured, restrained in tight fitting cuffs or manacles or whatever they might have been, he came close to what you're describing in freeing his hands and making good his excape. The soldier was commenting in awe of captive.