Hi Dom87,
The author's Eprom reader in your above link generate a hex dump with ASCII, which is then send to your serial port on the PC. Therefore, each 8-bit Eprom data is sent as two ascii bytes, and the text file you can then capture in the terminal.
However, most disassembler would only accept a true binary file image for disassembling. You will then need to do a lot of editing before the disassembler will accept it. You can modify the Arduino sketch to transfer the HEX data continuously without extra data like ascii representation, linefeed or carriage return, but then you still need to process the captured file into a true binary file.
I don't know if one can send a binary values of 0x00~0xFF directly via the serial port.
Regarding the disassembler, I would recommend the DASMx Version 1.40. Just search for "DASMx Version 1.40" in Google.
edit: added disassembler info