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First, is there by any chance another wire just like it attached to the PSU that you can use instead (they sometimes come with some extras)? If so, just do that and you're good to go (unless it created a short - but you'll know that soon enough).
If you tore it out from the PSU and there's no other wire like it to use, then I suggest you either take the PSU to a reputable computer repair shop (not Geek Squad or anyplace like that) and have them replace the wire or simply take the opportunity to upgrade your PSU and replace the entire unit. I do this for a living and I would not attempt what you are considering - it simply is not worth the effort involved and the risks of not getting it right (and is certainly not the time or place to learn such skills ig you don't already have them).
Frankly, I wouldn't even get it repaired (for essentially the same reasons and because it may cost almost as much as a new PSU) and would simply replace it (they aren't that expensive depending on what you need) - but that's your decision to make. As it seems to be a laptop, perhaps it might be best to let a computer repair shop (or the manufacturer's repair department) repair or replace it as it is tough to get to (and you don't sound very gentle with computers and there's much more serious damage you can do). You need to get one that fits your computer exactly and with at least as much power as the prior one and is compatible with your system - to do that you need to contact the computer manufacturer's technical support department or website to get the specifications (or just get the replacement part from them because then you know it will work in your machine - or just send it to them and let them deal with it).
Since you provided no information about your computer, it's hard to tell how much it will cost or what you will need or how hard it might be to do on your own (if that's even wise). If you provide the manufacturer, make, and precise and complete model number, I will check around for you - but it may take a while to do that research. I will not provide the cost of the repair or replacement by others (or make recommendations on who you should use), but I may be able to get you an idea on the cost of the PSU itself.
I hope this helps. If you provide the information requested, I'll see what more I can do to help.