Orochimaru has taken so much blood in his life of illicit human research. You might think he'd have lab assistants for that, but it's actually very hard to requisition assistance when your projects are secret and criminal. So, you definitely can't trust whatever else he might've done to you, but when Orochimaru is drawing blood it's for the same motive as any doctor: he wants to see what's going on in there. The only scenario in which he would be untrustworthy in drawing blood is if he's making mistakes with it to fuck with you. Which. Hm. Yeah. He might.
I still think he's your best option.
Bood drawing skill: 5
Blood drawing trustworthiness: 4.5
9.5/10
Zetsu is... some kind of plant. However, despite his planty nature, he has cared for and kept a variety of humans over his long life! He can probably do this, actually, and on occasions upon which he has attempted it, he has likely been quite trustworthy indeed. You could do a lot worse than Zetsu in this task. (Of course, what he's going to then go and do with your blood sample is not under discussion...)
Blood drawing skill: 4
Blood drawing trustworthiness: 4.5
8.5/10
Sasori is very skilled at this because, as we know, he removed all of his own blood and replaced it with gears and poison. However, Sasori is not a very trustworthy drawer of blood, and has little regard for others' bodies. He will get the vein the first time every time, but he might not take much care throughout this process. Any trustworthiness is related to his pride in his own skills, but since he's removed all the parts of his brain responsible for processing that shit, you might as well flip a coin.
Blood drawing skill: 5
Blood drawing trustworthiness: 2.5
7.5/10
If Itachi is for some reason trying to draw blood out of you with a needle, he's probably concerned about your well-being. If he just wanted the blood, he'd use a knife. He wants to get it right and he'll be embarrassed about hurting you if he doesn't, an emotion he'll have to cover up with some deep-voiced philosophy. However, drawing blood isn't a specialty of his — he has more self assurance than he does actual experience. But I'm giving him 1.5 points in the skill because he's, you know, Itachi.
Blood drawing skill: 1.5
Blood drawing trustworthiness: 5
6.5/10
Nagato probably needs to do this for himself sometimes. He was not looking very healthy when we saw him, you know? He has probably done this, but his only practice is on himself. Nagato is also very powerful and desperately selfish, so... well, he has no reason to hurt you, but he also has no incentive not to. He shouldn't be your first choice, but he might do in a pinch.
Blood drawing skill: 3.5
Blood drawing trustworthiness: 2
5.5/10
Kisame will not pretend to you that he has any skill at drawing blood (in the phlebotomy sense, anyway). He does not go in for telling random lies to strangers who, presumably, need his help. But if you need him to do it and he likes you enough to give it a shot, he will genuinely be trying to do it well. Very trustworthy.
Blood drawing skill: 0
Blood drawing trustworthiness: 5
5/10
Konan is not particularly interested in this task and can't be pressured into doing a good job for you through ego, money or interpersonal interest. She scores so highly strictly because I think she's helped Nagato do it, especially early on.
Blood drawing skill: 2.5
Blood drawing trustworthiness: 2
4.5/10
Deidara has never once had to draw blood, and the chances of him getting bored or annoyed are way higher than they are with some of these other characters. Nevertheless, he's not big on secondary motives and he dislikes the embarrassment of being bad at things. He'd try his best to do it right — for his sake, not yours.
Blood drawing skill: 0
Blood drawing trustworthiness: 4
4/10
Kakuzu is neither particularly trustworthy nor particularly skilled with a needle — I was going to point to all his sewing, but he doesn't actually use a needle for that. So he would be finding veins with a totally different tool. He is pretty used to taking apart human bodies and investigating their insides, though, and there might be some transferable capability between his threads and a phlebotomy needle. If you offered him money, he'd give it a go, and he wouldn't fuck it up just to entertain himself. But I don't love your chances of success — and, worse, he might not be happy with you if he fucked it up, and that would be dangerous for you. Only pick Kakuzu if your other option is, like, Hidan, okay.
Blood drawing skill: 1.5
Blood drawing trustworthiness: 2
3.5/10
Tobi would be bad at this. It's a careful and fiddly task and we have all seen how Uchiha Obito can fuck things up a gazillion times before he gets them right. He might also fuck this up for fun. Teehee. Or, worse, Rin's history as a medic means you run the risk of a misty-eyed flashback, which will then be derailed into Stupid Tobi Antics while Obito tries not to think about it. None of this is a good time for either of you. But he has certainly seen this done to himself many times while under the dubiously tender care of Zetsu and/or Madara, and perhaps sometimes while his sharingan is active. I'm giving him 2 in skill for that, because the sharingan is kinda bullshit like that.
Blood drawing skill: 2
Blood drawing trustworthiness: 1
3/10
Hidan finds your suffering compelling and he likes to watch it happen. He also doesn't even use a needle to reattach his own body parts, because he leaves that up to someone else. So not only does he have zero interest in helping you, he also has zero skill in doing it. You could assign him this task as a matter of vital mission-critical importance and he'd find a way to get an air bubble into you.
Don't pick Hidan. You could have two broken hands and no experience and still do a better job than this guy.
Blood drawing skill: 0
Blood drawing trustworthiness: 0
0/10