If I understand correctly, that would have to be done before the magazine was shipped into NY state, so "you" can't do it, the seller would have to
You are right that he legally can't, but it
can be done within NY. I had mine done by the FFL that I bought the gun from. He happens to be a deputy sheriff and that may be the difference. Large cap magazines are legal for LEO, so obviously someone can bring them into the state. You just have to find the right person. If the OP lives anywhere near Canandaigua, NY I can give him the name of the person who did mine. Otherwise you will either have to find an FFL that will do it or have it down before it's shipped to you.
However, if you can just buy 10 round mags, that's easier and you can probably have the gun seller sell the large mags.
Before the SAFE Act passed, pre-ban large cap magazines were legal and all Open and Limited division USPSA shooters used them. When the law passed they all had their magazines pinned or blocked. I believe most did it themselves.
I don't know the exact wording of the NY law, and that WILL make a difference.
Here is the relevant code. When reading any of these codes you need to read all relevant other parts because they may add on, subtract, and/or exempt parts of other codes. I say this because the first part of this mentions magazines manufactured before 9/13/1994 and is referring back to 265.02, paragraph 8. Remember, you shouldn't watch how laws or sausages are made.
S 265.36 Unlawful possession of a large capacity ammunition feeding
device.
It shall be unlawful for a person to knowingly possess a large
capacity ammunition feeding device manufactured before September
thirteenth, nineteen hundred ninety-four, and if such person lawfully
possessed such large capacity feeding device before the effective date
of the chapter of the laws of two thousand thirteen which added this
section,
that has a capacity of, or that can be readily restored or
converted to accept, more than ten rounds of ammunition.
An individual who has a reasonable belief that such device is of such
a character that it may lawfully be possessed and who surrenders or
lawfully disposes of such device within thirty days of being notified by
law enforcement or county licensing officials that such possession is
unlawful shall not be guilty of this offense. It shall be a rebuttable
presumption that such person knows that such large capacity ammunition
feeding device may not be lawfully possessed if he or she has been
contacted by law enforcement or county licensing officials and informed
that such device may not be lawfully possessed.
Unlawful possession of a large capacity ammunition feeding device is a
class A misdemeanor.
The key factor is the interpretation of what "readily" means. It seems to be used in other laws and states, but is never defined. I and others choose to take it to mean quickly or on-the-spot. If you need to cut a rivet or unglue the base plate (mine are hot glued), then that probably meets the definition of "not readily." If they meant "not ever" they wouldn't have used "readily."