I was running Peppermint Linux on this laptop, it's got 2GB RAM and dual core CPU so it's not the slowest of wheezy laptops, but it's not blistering either. I think it's about 15 years old.
Anyway, I've tried installing Lubuntu 18 "Bionic Beaver" and this seems to run better on the laptop than Peppermint did - seems snappier to use.
Using that, I've tried TapeUtils in Java again and successfully loaded 3D Monster Maze into my ZX81 for the first time in 30 years
A bit more tinkering is still needed (I had some other 16K programs fail) but there's progress.
Thanks for all your help, I shall be looking into some of the suggested programs later