If the NDT is informational only, i.e., not required to meet code and not reported to the customer, there is no need to be certified.
I provide training to welders on a regular basis so they can check their own work, but they are not performing the NDE as part of a documented inspection or test. It is not a contract or code required NDE.
The first step your company has to take is to develop a Written Practice. Your employer should retain the services of a third party (outside agency) to help with that task. The WP should address all the requirements of the applicable NDE standard, in your case MIL-STD-410.
The WP will define the requirements for qualification for initial qualification as well as the steps to become certified. The WP will also address how certification is maintained, how certification can be revoked, terminated, as well as reinstated. The WP will stipulate how many hours of classroom training (or homestudy) is required, the required relevant work, and the required examinations and test scores required for initial certification as a Level I, II, or III.
A system should be instituted to maintain a record of your training activities, O-J-E, examinations, etc. to provide objective evidence you have met the qualification requirements for initial certification as well as for the maintenence of your certification.
The WP will have to be reviewed and approved by your customer if you are involved in military contract work.
Since your employer does not have a Level III on staff, they will have to retain the services of an Outside Agency to develop and administer your qualification and certification program. The same Level III can also develop the NDT procedures you need to perform those NDE required by the purchase order (contract, project specification, drawings, etc.). The NDE procedures will also have to be reviewed and approved by the customer before being implemented. The Level III your employer uses has to meet the same qualification and certification requirements stipulated by your customer. That is, they may request copies of the Outside Agencies written practice, procedures, training outlines, certifications etc., which are subject to your customer's review and approval.
I hope this helps.
Best regards - Al