It seems it's rather difficult to just do it, given that these wounds are typically surrounded by hesitation marks and how uncommon it is, and the cut needs to be pretty deep, but...
It depends on the cut. It could take minutes to bleed out done optimally to a major artery. Smaller injuries could take hours. Very painful until you pass out.
Success rate is very variable as well depending on the injury you inflict, and whether you are going to get up and take yourself to the hospital (or someone will take you) if you fuck up. You can find descriptions of the incision if you search papers, there are some publicly available - and there are things that protect your arteries, hence the need for a very deep cut.
Hanging seems vastly preferable. It's very hard to imagine a person for whom hanging wouldn't be an option but cutting their throat would be, unless they were fine with any other unreliable and painful method too. Why is hanging not an option for you? If it's that it's technical, this method is not for you. If it's that you can't have time alone, this method is not for you.