What bluetooth chip should be purchased to solder onto the Nook motherboard?
You can use any uart capable device that has a logic level serial port and operates on 3.3V.

Only three pins of the U2713 connector are needed. (4 are needed if you need to supply 3.3V to your serial device.)

It would be close to a miracle if some bluetooth module had a connector that mated directly with the pinout of U2713.

So, you are pretty much going to have to break out the soldering iron and attach wires to your Nook and your bluetooth device.

Use fine wire, and put a spot of hot glue or epoxy on the (grouped) wires to hold them in place. That is, bundle the wires, and glue the bundle down.