Replace the script with a wrapper that runs strace that in turn launches the original script. This might involve
mv yourscript /somewhere/else/yourscript and then yourscript becomes
#!/bin/sh OUTPUT_TO=`mktemp /tmp/yourscript.$$.XXXXXXXXXX` || exit 1 exec strace -o $OUTPUT_TO ... /somewhere/else/yourscript "$@" where ... is whatever other strace arguments you need.
As an alternative, consider sysdig, as it can trace by filename or username without the need for a process ID or wrapper script.