In preparation for the repair work expected on the SH-101 in particular, I anticipate needing to see the output waveform. Only considering audio signals, so there is no need to sample high frequencies.
The JYETech DSO Shell kit with sample rates up to 200KHz should do the job, and was a decent inexpensive project to get back into the swing of my soldering skills. I did find my old 15 watt soldering iron inadequate for soldering the large BNC connector, and so got hold of a 25 watt Antex (good to see the same brand going strong) which did the job.
Markus Fuller does a decent walkthrough of building this DSO kit.
My own efforts…
Used some tape to hold the screen down to stop it flapping about while still working on the boards.