I know a guy in Mississippi, but schlepping two chairs all the way there would be no picnic (he'd have to have the good one in person to replicate it on the missing one).

You don't want a carpenter for this job but rather a skilled woodworker with a deft touch to recreate this seat.
NYMag.com recommends Traditional Line
http://nymag.com/bestofny/services/2006/woodwork/

You can also try the Franklin Report
http://www.franklinreport.com/default.aspx?m=nyc

A good friend of my boyfriend’s is a woodworker - he is located in Brooklyn and mostly does high-end carpentry like custom wine cabinets and remodeling (he is just like the guy from Holmes on Homes when it comes to ethics in construction). His website is below (it states that his workshop is in NJ but he's no longer in that space). He may be more that what you need but I wanted to give him a mention since he had to shut down his workshop because he couldn’t compete with the construction companies who cut corners to give clients a better price.

http://jmowood.com/default.htm

Another option might be to put an ad on Craig's List.

Tyler at Codfish Park Design might be an option. He did some beautiful work in my apartment a few years ago.

http://codfishpark.com/

yikes! you don't need a carpenter, unless you think 'hideous' can be fixed...

And perhaps your manners, papyrus, can be fixed as well.

They're like Borg chairs, half organic, half inorganic...