I'm under the impression that Nexus 8 and Alfine 8 shifters and hubs straight interchange... but even if I'm missing something there, Shimano themselves says you can use the Alfine SL-S503 Rapidfire shifter with Nexus 8.
The problem here is the IGHs from shimano don't use a linear activation - you can't use any old shifter.
The amount of cable pulled between each gear are not the same.
So you need an Alfine or Nexus 8 speed trigger shifter for an 8 speed alfine or nexus. They do exist.
(not sure about the cable pull on 3 speed hubs sorry.)