Hi and welcome to the forum.
If you are assembling an electronic product and selling it to consumers in the UK or Europe, albeit by installing components in a reclaimed case, you will need to CE-mark it as complying with the relevant technical directives and standards such as LVD and EMC. You can do much of this yourself, although you might need to enlist the services of a test house to approve the overall device for EMC emissions etc. This is not onerous especially if your modules are in themselves compliant as stand-alones, but would have to be done for each different design or combination of components. Each unit of a given type would be tested on completion; what electrical testing is needed would depend on what your specification calls for. A conventional PAT might be suitable or not as the case may be.
This is a different situation to restoring a set to original condition, where provided the design is not materially altered and the work is done using good practice and in compliance with whatever regulations existed when it was made, no further approval need be sought.
I assume that the radios you are converting are the technically unrestorable examples where the original chassis is beyond practical repair? It seems a pity to dismantle original sets otherwise, as all reasonably intact valve radios can at present be restored to good working order and will probably still be working / repairable long after bluetooth technology is lost to history. It is often a simple matter to integrate the bluetooth receiver to the original circuit so that it can be used with a phone, but retains its authenticity and can be converted back when its value as an original collectable exceeds that of it as a novelty bluetooth speaker. Of course, not all chassis are worth repairing, just throwing the idea out there!