There is a very real possibility you will be extradited. The extradition decision regarding the individual warrants will be made each time you are picked up. The actual extradition decision is made at the local, not state level.

If you want a definitive answers then you must call the jurisdictions which issued the warrants and ask them. They may or may not discuss their extradition policies with you. If not, than the only way to find out is to be picked up in New York and see what happens.