Only potential problem is that NJ is a state where firearms ownership is only by exception from the many, many control laws we have in place here.
As noted above the law first prohibits possession then provides various limited exceptions only.
Without documented proof that the pistol belongs to you, the police can, if they ever become involved, seize the weapon until you provide sufficient proof to their satisfaction.
As an example, on one occasion, whilst driving with a colleague from our homes to a range for target practice we were involved in small traffic ding where we were rear ended.
When the local PD arrived and they asked us where we were going we had to provide our FID's and our handguns were going to be seized and held until we could "prove" they were our property.
Being aware of the potential issues, this having happened to fellow shooters before, we both keep a photocopy of our Permits to Purchase for each handgun in the gun case. It was only after being held for another 30 minutes whilst this was "being checked" were we finally allowed to go on our way.
Whilst I understand your desire to keep the pistol "off the grid" you need to be aware of the potential issues.
If you want to go down the registration route the form link is attached below.
http://www.state.nj.us/njsp/info/pdf/firearms/sp-650.pdf