The DNA test results, taken from a non-invasive mouth swab sample, could be emailed or posted to Banks in just five days.
The test would conclusively eliminate Banks as Shaw's blood relative if it showed a negative result, or prove paternity to an extremely high scientific threshold should it produce a DNA match.
"If you have the mother, it's one-in-a-billion," DNA Solutions director Vernon Muir told the Herald.
"If you don't have the mother it's in the hundreds of thousands, so it's still incredibly accurate."
Banks did not appear today when the case had its first call in the High Court at Auckland.
He was not represented by a solicitor and has not responded to Herald requests for comment.
Justice Tim Brewer suggested to a media-packed courtroom that a simple DNA test could resolve the paternity dispute and prevent the expense of a costly trial.
Muir said such tests were easy to arrange. To meet the evidential threshold for court, they had to be carried out by an accredited lab and meet strict "chain of custody" requirements.
A standard "peace of mind" test cost $299. But the legal test was $699 as each step was vigorously documented and subject to random auditing.
If Banks chose to take the test, the lab would also need a specimen from Shaw.
"They don't have to come in together. We would just organise for a sample to be taken from [Shaw] and we'd organise [Banks'] sample with a lab at his closest location and they wouldn't have to do anything else."
DNA samples could also be extracted from discarded cigarette butts, licked envelopes and fingernail clippings, though these could not used as evidence in a legal test.
If the paternity case is successful, Banks could be declared Shaw's next of kin with legal implications relating to potential claims against Banks' will.
Today's hearing heard that Shaw's legal team, headed by Lowndes litigation partner Jacque Lethbridge, had encountered difficulties in serving documents on Banks, who they say has not engaged in attempts to resolve the claim.
Brewer adjourned the case for a fortnight and made an order allowing documents to be served on Banks' solicitor.
He said if Banks had been unaware of today's hearing, subsequent media coverage meant the controversial politician would now "know what's going on".
After referring to the enormous costs of a full trial, Brewer said: "There's some suggestion that Mr Banks doesn't want to have a DNA test."
Lethbridge replied there had been attempts to have Banks engage on the question of whether he was Shaw's father, and that a DNA test could ultimately eliminate him from any paternity claim.
"The evidence is that he didn't engage in that."
People cannot be compelled to provide DNA evidence in paternity cases and Shaw is not seeking any such order from the court.
Shaw, who now lives in Japan with his wife Noriko and son Kent, has said the case is not about money. He simply wanted certainty about his ancestry for him and his family.
Outside court, Lethbridge said Shaw first learned that Mr Banks was likely to be his father in 1999 "and he's been trying to establish that ever since".
"I can confirm that my client has either personally or through family members tried to have this matter clarified with Mr Banks but that has been unsuccessful.
"Most reasonable people faced with this scenario ... would probably try and get to the bottom of it without the need for putting people through the cost of a High Court proceeding and the embarrassment that might follow."
She reiterated that Shaw's birth father information was blank on his birth certificate and he wanted his son to have certainty as to his paternal grandfather.
Shaw grew up believing his mother's Asian partner was his father.
His mother is alleged to have had a relationship with Banks in the late 1960s while working as a nurse in Hamilton.
She eventually told Shaw about his parentage in 1999 and he tried to meet Banks in the early 2000s during a trip home from Japan to ask the then mayor "are you my father", a 2001 women's magazine article alleged.
University of Otago law professor Mark Henaghan told the Herald paternity cases like this were rare.
They were more usually taken by women under the Family Proceedings Act for child support purposes.
Applicants would need to produce strong circumstantial evidence to prove the two parents had been in a relationship at the relevant time, often in the form of sworn affidavits and photographs.
A court could draw "adverse inferences" if a person refused to take a DNA test, Henaghan said.
