Oh, the HS injector might help a little in healing wounds, but not to the point of regenerating whole limbs.
Having access to an HS tank would be pretty convenient for the gravity of those wounds, but you don't. This said, most nekos attempting to reattach their limbs will usually be able to have their flesh rebond in minutes (though the actual fixing of nerve endings, blood vessels, bone fusing back together and such takes much longer).
With Hasegawa Sumaru, the samurai had one arm severed off by the way of cutting into his shoulder diagonally from collarbone to armpit and then through the lower deltoid muscle until the arm had nothing holding it and just fell down. That missing arm would be a problem to put back together, but on the other hand he's a NH-27 - it hurts, but he can work without it.
Kotori, for some reason, seems far more interested in him just being awake... which makes an application of stimulants to wake him up the likely solution.
Akiko's limbs is likely one that can just be put back together the way I explained before. Not a perfect solution, but at least it's better than just having a bleeding stump.
Reika might be the person in the most need of an HS injection. She's the one who took the worst beating while yet not losing any bodyparts. It doesn't mean she's not in bad shape, though - she did take two direct gunshots, and suffered from several more proximity explosions. Fuyu and Akiko would come second, also having sustained gunshots.
Kyoko severed torso is somewhat beyond a simple medical kit. The halves of her body could be put back together but that won't easily fix the disarray of her guts having been cut through with a sword. Reika had the right idea: her body will mitigate any bleeding, but the wound is still mortal - without an HS tank to regenerate in she's as good as dead. Having an ST backup could be something that would be done to save her mind if she cannot be treated; she'll still die but if respawned she'll keep all her memories.
Sora is a really difficult case because it involves a lot of burning someplace important, which makes Konoka's medkit rather ineffective at treating that mortal wound. However, it seems Kotori has a plan - she just needs Sumaru conscious to make it work.