My decoder recently died so have been toying with replacements ideas that would also incorporate some sort of serial interface to the computer

The least soldering and building or thinking too hard.....
An old computer with built in serial interface is probably the easiest thing using optocouplers and say heavy metal as your (go between) 
Its pretty easy to find an old computer with built in serial. To tell if its suitable run heavy metal on it with a loopback to pins 2&3 on the serial port at 45.5 baud
If that computer sends what it receives then "Nagle's" board at https://www.aetherltd.com/connecting.html would be your magic device interface.
All the parts for that board are available.

Arduino...
Lots of solder, cerebral usage, wires laying all over the place and programing......................
I started playing with arduino's recently because as I stated my decoder died and I wanted something a tad more sophisticated to do the decoding and to have some sort of serial interface too would be nice to send to the teletype from computer all in one box instead of two boxes I had. My prev decoder ran the teletype and would put the text on a video monitor and it was about 30 years old. I also had on the loop a serial interface and would sometimes get a mess if both talked at the same time.
On the arduino front I have the Sending from the arduino down pat. Decoding from the loop I just got working. Now I need to add a second "loop decoder" and feed demodulated RTTY input into the second loop decoder is the project for this weekend...