NY I do believe is 6 years for the Statute of Limitations. So I think you are ok. If you dont' want to pay it then send the CA's a cease and desist letter stating the debt is beyond NY's Statute of limitations.
But there is a catch though. This does not forbide them to try and sue, in hoping you don't show and they are rewarded a default judgment. It's a shot in the dark for them and they are succesful. If by chance one of the CA's try and sue, YOU MUST ANSWER THE SUMMONS as the debt is time barred as your defense and plan on showing up to court NO MATTER WHAT, even if the CA say's it will drop the case, plan on showing up anyway.
This also doesn't prevent them from selling your debt to another junk debt buyer, so you will always have to keep an eye on your mail, you have to keep on top of all three of your credit reports to make sure there aren't reporting.
When debts are beyond the SOL's CA's hope that most consumers don't know their rights, that there is such a thing as SOL on bad debts and also hope they ignore any summons. You also have to remember that it is up to you as the defendant to prove that the debt is out of the SOL. so if you don't have any records from your Credit report get them and keep them safe and sound. And any past records of your debt as well. It's not as easy as just telling the judge, "It's too old to collect on", he'll so OK how old is it. The attorney for the CA isn't going to tell the judge.
Now I'm not saying this is going to happen, but it could and you just have to be prepared. There is no SOL on attempting to collect on debt just on when they can legallly obtain a judgment against you. so just have all your ducks in a row. Using the SOL to get out of paying a debt can work but you will always have to keep looking over your shoulder, and always staying on top of your credit report.