1. First of all, I know nothing about that type of adapter card you mentioned so I can't comment on whether that's some sort of viable solution in your situation. Perhaps another responder to your query has some info on it relative to your objective.
2. One possibility occurs to me. Assuming you have or can get your hands on a USB external enclosure (or one of those SATA-to-USB adapters) and you have a HDD (or SSD) sufficient to contain the present data contents of your installed M.2 SSD...you could utilize a disk-cloning program to clone the contents of the M.2 drive to the USB's external drive.
(I'm not sure I quite understand your comment that you "want to still be able to pull files from the old SSD". If you're able to clone the contents of that drive, *all* the data will be copied to the new drive. You understand that, right?).
3. Then install the new M.2 drive and using the above apparatus clone back the contents of the USB drive to the newly-installed M.2 drive.
4. Does that sound like it might be a viable solution? The disk-cloning program we generally use - Casper - does, however it's a commercial program costing $49.99. (It's the best d-c program we've ever used; we use it primarily for frequent/routine backups of our systems because of its speed, simplicity of use, and general effectiveness. And, of course, we also use it for "one-shot" type of disk-cloning operations such as the one in which you're interested.
Casper does have a 30-day Trial Edition available so you may want to give it a try if you think the disk-cloning approach is a practical one. See...
https://www.fssdev.com/products/casper/trial/
There are quite a few freely-available d-c programs. The Macrium Reflect program is quite good in our experience as well as the Easeus Todo and AOMEI Backupper programs that we've also experienced.