I happen to volunteer at the Putnam County Historian's office and did a quick look-up for you for the names of judges in Putnam County in 1843. I found 3 names for you.
Bennet Boyd, Daniel Kent & Cornelius Warren.
Bennet Boyd is buried in Carmel, Cornelius Warren in Philipstown and Daniel Kent in Patterson. They were all acting Judges in Putnam in 1843. I couldn't find anything to their connection to the Baptist Church in Carmel. I would guess that Bennet Boyd, since he lived the closest, could be the name you are looking for.
If you need more information, email the County Historian. The staff there could do some additional research for you. www.putnamcountyny.com/historian
Hope this helps,
Liz