What's the best printing technique to produce splints (a device to immobilize a body part)?
For anything where there is an open or bandaged wound, you should NOT use 3D printing, and should use sterilized medical equipment to prevent infection and heavy metals infiltrating the bloodstream.

SLA/SLS 3D printing may be the best option for replicating the complex structure of the splint you have pictured above, as FDM printers have difficulty reproducing those structures.

However, FDM printing CAN reproduce it, and generally FDM printers have access to a wider variety of materials of which models can be printed with, so they may be the best option overall.

For something to immobilize a body part that has been broken, you may want to use a stiff material such as ABS or Carbon Fibre, However PLA may work still in these cases.

As for something to support a body part, Flexible or Semi-Flexible materials may be desired, such as Ninjaflex (TPU), Nylon.

As a disclaimer:
I am not a medical professional, This is not medical advice, please consult a properly licenced medical professional first before using 3D printing to solve a medical ailment.