Welcome to the forum!
The short answer is no, you will not be able to read it in the injector.
This has been discussed several times on the forum before, I would recommend having a bit more of a read then asking clarifying questions if you cant find anything 
anyway to answer your question in more detail:
It is possible to sometimes read the 125 kHz LF tags inside the injector due to the magnetic coupling but with the HF chips like the spark you will have no luck. The implant is actually stored in the needle which acts as a Faraday cage essentially. The skin effect also comes in to play.
@Pilgrimsmaster as well as a few others live in NZ they might have some local advice. This thread is fun, has locations of quite a few forum members around the globe.
In regards to self install, the large flex chips would be challenging, there are some who have done it on here but it limits install location for instance good luck putting it on your dominant side. The X series however is more commonly self implanted this video is a popular guide from SparkFun.