By definition, all implants are invasive...
Assuming that our surgeon is working under the table in an effort to supply illegal aliens with counterfeit implants, and that whatever complexities involved in the process of making the devices is handwaved, the actual surgical procedures are quite simple.
We'll assume two devices: one is very small, no larger than an 80mg aspirin pill; the other about an inch long and a square centimetre in cross section. We'll also assume that the devices are sterile!
1. The first device is easy to implant: a needle is inserted into the tissue below the occiput and aspirated (you don't want to put the implant into a vein!). A guide pin is then inserted down the bore of the needle, which is removed. A series of increasingly large cannulas are placed over the guide pin. These will create some space for the implant injector. Lastly, the injector itself, with the implant loaded, is placed over the guide pin and the handle depressed. The implant is safely lodged within. A dab of tissue glue helps hold the implant in place. May or may not need a stitch. A little skin glue should be sufficient on the surface.
2. 98
The second device will require a little more work. Basically, make a stab incision in the umbillicus and use a clamp to create a pocket within the subcutaneous tissue. Suture the device to the person's tissue (prevents inadvertent or intentional removal) and stitch up the fascia. Will probably require a single stitch or two in the subcutaneous layer and maybe some skin glue.
3. Your country is very weird! I've got no idea where exactly, "below the belt" implies. The actual procedure will be very much like one of the above.
Ah, yes the issue of pain. Well, your "patient" is an illegal alien trying to subvert the law. A little pain won't do him any real harm.
Cold packs are a good start. There is a minor analgesic effect with the cold. Other than that, I'd suggest the use of nitrous oxide. Perhaps a little midazolam. Patient will feel discomfort and pain, but really won't give a damn! Just keep them comfortable until they're safely out of the clinic!
An actual veterinary ID implant:
And its insertion device:
This implant is absolutely huge compared to the suggested device, but you can see ho the pocket is made and the device is seated within: 75