If you use a runscript, and the runscript calls "exec wine myexe.exe" in the container, then outside the container you should be able to do:
singularity run container.simg
and actually, if you just execute the container, this does the same thing:
./container.simg
the reason being if you look at the head of the file, you see this:
#!/usr/bin/env run-singularity
Which tells your system to execute the file using the run-singularity executable, which is the other executable in the singularity bin.
If you are needing to use "singularity exec" because you only have one runscript/entrypoint and want to define more, then the single runscript isn't sufficient and you would do well to put your stuffs in a
Scientific Filesystem (SCIF):
And then to run your different apps you could do like:
./container.simg run ping
./container.simg run pong
./container.simg run oregon-trail
etc.