As you pointed out, it's backordered in a lot of places, plus you need quick delivery. If you could order and have it FedEx'd that might beat some of the Christmas backup, but you'd still have to be confident that it truly is in stock and the merchant will ship immediately.
I've heard of places that send you the code. Some may not be reputable, but one -- I can't remember which -- is mentioned by a prominent Resolve Youtuber. I think they open the package and type the codes into an email for you and I'm assuming after a while they destroy the card.
There are several YouTube videos online about how to do some amount of noise reduction in the free Resolve and most use the RemoveNoise node in Fusion. The first guy (who is really great for color grading tutorials) first does it with Studio's Color NR, and then does it with Fusion so you can see side-by-side. The second guy also uses RemoveNoise in Fusion, and adds an Unsharp Mask to try to restore a little perceived sharpness back:
Bottom line is that you're bluring stuff and then sharpening to try to tame things. It's more effective for chroma noise, since perceived sharpness is in the luma.
There's also a technique in Color where you convert the video to Lab color space, then split it, blur just the chroma (a and b) and then join it back up and convert back from Lab colorspace. That's basically what the RemoveNoise is doing too, and it takes 5+ Color nodes so it's more complex unless you're a Color guru. On the other hand, Color makes it easy to mask/qualify portions of the image to affect while Fusion is more complex in that case, so if you need to affect just a particular portion of the image Color could be easier.
Last, there are dedicated plugins that you could probably order online and download maybe in the $100 range. Neat Video is mentioned favorably in these forums. Plugins work in the free Resolve.
(Worst-case scenario, you could try (free) Handbrake's denoising. It can do spatial and temporal denoising -- which is what the Studio Color NR uses -- though it's not as sophisticated and obviously you're either running individual clips through it and bringing them back into Resolve or you're going to use it on the entire video output from Resolve which is going to probably not work so well, since each clip/scene probably needs a different level/kind of NR, if it needs it at all. It has two denoisers and the NLMeans option is newer and better.)
Good luck!