Why did the officer stop you in the first place? It would be nearly impossible to have probable cause to believe your registration was not signed prior to stopping you. An officer has to have a reason for the contact in the first place.
The officer will have filed an affidavit under oath stating that the registration was not signed. Presenting a signed registration after the fact will not show that it was signed on the date of the ticket, unless you can also testify that it was actually signed. Even then it will come down to who the judge believes. If you falsely testify that it was signed at the time you will be committing perjury (a felony).
You're more likely to beat this ticket, as with almost any ticket, on the Court Rules, Rules of Evidence and Rules of Procedure, than the facts.
As far as how you should fight the charge in court, the Washington Bar Association prohibits attorneys from assisting non-attorneys in the practice of law. Answering questions about the law for informational purposes is fine, but you will not get an answer as to how to proceed with your case.
It is not clear to me from your question which statute you are being charged with violating. If it is only an infraction, you can request a contested hearing within 15 days. Depending upon the court and the charge, it is unlikely a judge would just dismiss merely upon a showing that you now have proper registration. You would likely need to present some motions and or sound legal argument to overcome the relatively low burden of "preponderance of evidence." Unless there is an obvious error in the evidence, the better course of action would probably be to try to negotiate a settlement with the prosecuting authority. You could do this on your own, but this is the type of thing an experienced traffic infraction attorney could probably handle more competently. My firm does this type of work all the time.
If this is a criminal charge then you should definitely contact an attorney before trying to resolve this matter on your own. Even a minor criminal traffic charge can have long term consequences.
Officer must have been mad at you or something. There is such a law and you are required to sign it. If you show up at the hearing and tell the judge that the tabs people did not tell you to sign and you just paid and put it in the glove box and signed it when the officer brought it to your attention the judge might dismiss but impose a $25.00 fine (since it was not signed). I have never attended a court hearing on this topic - but, the law says it has to be signed. The judge also has the power to dismiss it and may. The times I have seen an officer cite someone for this - someone talked back or the stop was pretextual. You might be able to make a pre-textual stop argument. However, it would depend on that the officer statement said was the reasons for pulling you over. Contest the ticket and ask for a copy of the police report. You are also allowed to change the hearing to a mitigation hearing at the time of the hearing. Under either circumstance, bring the registration and show the judge it is signed. A copy is acceptable.