Unfortunately, yes. You will be required to register, as per Megan's Law.
Here is the law at this link and it reads as follows:
2C:7-2. Registration of sex offenders; definitions
a. A person who has been convicted, adjudicated delinquent or found not guilty by reason of insanity for commission of a sex offense as defined in subsection b. of this section shall register as provided in subsections c. and d. of this section. A person who fails to register as required under this act shall be guilty of a crime of the fourth degree.
b. For the purposes of this act a sex offense shall include the following:
(1) Aggravated sexual assault, sexual assault, aggravated criminal sexual contact, kidnapping pursuant to paragraph (2) of subsection c. of N.J.S.2C:13-1 or an attempt to commit any of these crimes if the court found that the offender's conduct was characterized by a pattern of repetitive, compulsive behavior, regardless of the date of the commission of the offense or the date of conviction;
(2) A conviction, adjudication of delinquency, or acquittal by reason of insanity for aggravated sexual assault; sexual assault; aggravated criminal sexual contact; kidnapping pursuant to paragraph (2) of subsection c. of N.J.S.2C:13-1; endangering the welfare of a child by engaging in sexual conduct which would impair or debauch the morals of the child pursuant to subsection a. of N.J.S.2C:24-4; endangering the welfare of a child pursuant to paragraph (4) of subsection b. of N.J.S.2C:24-4; luring or enticing pursuant to section 1 of P.L.1993, c. 291 (C.2C:13-6); criminal sexual contact pursuant to N.J.S.2C:14-3b. if the victim is a minor; kidnapping pursuant to N.J.S.2C:13-1, criminal restraint pursuant to N.J.S.2C:13-2, or false imprisonment pursuant to N.J.S.2C:13-3 if the victim is a minor and the offender is not the parent of the victim; knowingly promoting prostitution of a child pursuant to paragraph (3) or paragraph (4) of subsection b. of N.J.S.2C:34-1; or an attempt to commit any of these enumerated offenses if the conviction, adjudication of delinquency or acquittal by reason of insanity is entered on or after the effective date of this act or the offender is serving a sentence of incarceration, probation, parole or other form of community supervision as a result of the offense or is confined following acquittal by reason of insanity or as a result of civil commitment on the effective date of this act;
(3) A conviction, adjudication of delinquency or acquittal by reason of insanity for an offense similar to any offense enumerated in paragraph (2) or a sentence on the basis of criteria similar to the criteria set forth in paragraph (1) of this subsection entered or imposed under the laws of the United States, this State or another state.
I suggest that you can consult with a local NJ attorney about possibly petitioning the NJ Courts for a waiver to register. I am not certain on what basis that might be granted, but it is always a possibility.