Some further searching and applied logic resulted in something less involved and more practical. Here is what you do:
Find a microwavable plastic cup. I use one of the little Tupperware tubs that some takeaways give you sauce in. Place your shards of old soap in the cup, having removed any labels the soap may still have.
Take a metal teaspoon and carve a trough in one side of your new bar of soap. Put the soap you have carved out in the cup with the old soap.
It does not matter if the soap in the cup is wet, but be sparing if adding extra water. Spend a couple of seconds crumbling the soap so none hangs over the edge of the cup.
Place the cup of soap in a microwave and give it 30 seconds. Keep an eye on the soap and stop the microwave as necessary. I put a little too much water in with the soap and it frothed over the side of the cup. The turntable was due for a clean anyway.
If the soap is not sufficiently softened/ melted, give it additional bursts of about 10 seconds until it is how you want it.
Take the teaspoon and use it to pack the soft soap into the trough on the new bar of soap. I ended up taking a foil wrapper and encircling the soap with it to pack it down. The wrapper was used food packaging so additional points for recycling and repurposing!
Let the soap cool before you attempt to remove the wrapper if you used one. Very little soap should adhere to the wrapper if you have waited long enough.
I was a little concerned I had used too much water so I put the bar in the freezer for a few hours in the hope that some of the excess would crystalize out.
I tried the bigger bar of soap today. Works perfectly. The little plastic tub now lives in the bathroom, ready to collect future shards of soap. Currently my bar of soap rests on top of it to dry. When it gets smaller I will place it on a repurposed shampoo bottle cap.
Discovering soap can be melted in a microwave offers some interesting potential. Soaps can be made with essential oils, fruit zest, oatmeal or various other additives. I seem to recall I once saw coffee soap advertised. There is always a little bit of coffee and grounds left in the pot. It is mince pie season so some of those foil cups may get repurposed as moulds.