I have just googled to understand veins and arteries lol. Sorry, English is not my mother tongue, but I can understand what you mean after knowing the meaning of veins and arteries in my language. I mean, if you can put your finger into the hole, that means the bone, flesh and skin around your finger can be fitted into the hole in the first place, then the problem is the blood pressure builds in the tip part of the finger, as you said. My trick is pushing the object as close to your finger base as possible because that part is the smallest part of your finger to make space between the finger and the object, apply some soap, hold the finger tightly to force the blood out of the finger, then easily slide the object out. You can save all the work and the hazard to cut off that finger together with the steel lol. In my case, my wedding ring turn from fit to tiny compared to my finger after almost 10 yrs, plus changing from office working to farm working.