OK, be aware that if you are not using a pre-certified module then you will need to go through an extra set of radio testing. I've not done it myself, but I understand it will add quite a substantial cost to the certification process (several times more than the usual emissions/immunity tests). I suspect Nordic can help with some low-level radio control firmware needed for the testing. Espressif have something similar for their ESP32 chips.
Yes, a lab can help with these tests - but not all labs are accredited for all tests, so they sometime outsource or just shrug their shoulders. BTW, I think CE is officially called RED now. Like C-Tick is now called RCM, and IC is now called ISED, etc.
Another thing is if you are using Bluetooth technologies, you probably need to join the Bluetooth SIG as a (free) member and then pay for certification of your product to use the BT patents & trademarks. This is something I have done (membership), and my company has been allocated a unique identifier for when I was working with Bluetooth Mesh. See
https://www.bluetooth.com/develop-with-bluetooth/join/It is interesting to scroll through the assigned company identifiers, particularly noting companies you may know of who only joined relatively recently...
https://bitbucket.org/bluetooth-SIG/public/src/main/assigned_numbers/Also, I just thought of something else. As this is a wearable, you may have to do SAR testing. Another significant cost if it is needed. And you really wouldn't expect that is as there are plenty of other nRF52 based wearable designs, and any mobile phone transmits at much higher power but yet must have passed. I don't know if you can use that reasoning, so you may need to have the tests done as proof of meeting the requirements. Again, I've managed to avoid projects needing this (other than some concept prototypes that didn't go further).
Here are some references - but I suggest you find a local lab/consultant to help you:
https://www.rfexposurelab.com/sar-requirements-for-wearable-technology/https://www.ul.com/services/wearable-technology-testing-and-certificationhttps://www.tuvsud.com/en-us/industries/consumer-products-and-retail/wearable-deviceshttps://www.reddit.com/r/rfelectronics/comments/1ednpqy/esp32_wearable_sar_test/Once you work your way through that minefield, I don't think there is any real restrictions on who does your manufacturing - after all you aren't making medical/automotive/aerospace products??? Up to you if you want to use someone with ISO9000 or similar for QC processes. But you should also note that the certification is only valid as long as the finished product doesn't vary in any "significant" way from what was certified. If you make revisions (to schematic, PCB, BOM, even the housing design) then you need to analyse the potential effects to determine if the change is significant and requires re-testing. Fun stuff.
Maybe check out the updates from the SlimeVR project as they talked about a bunch of these topics, and they may be willing to chat with you more if you reach out to them. I can't recall if they did SAR.
https://www.crowdsupply.com/slimevr/slimevr-full-body-tracker/updates/In the end, this is all about risk management. It helps with paperwork problems with shipping (one of the earliest and most visible issues you could encounter), and provides protection from potential government enforcement (or private action) if you have done something horrendously wrong in your design or paperwork.
I've likely forgotten something else... and maybe even misstated something unintentionally. The above is only worth what you paid me for it (nothing)... so please do you own research and get professional advice.