How to remove a file without using rm?

The unlink command is also part of POSIX:

unlink <file>

Are you able to run shred? If so, then:

shred -u <file to remove>

Is there another method to remove a file without using rm?

busybox rm -f path/to/file

This is assuming your scheduling application allows you to run busybox unrestricted. Since you haven't specified which application it is, we don't really know what the restrictions are, but the above should work if the application has a simple molly guard preventing execution of just rm.