There is no straight-forward way to do this. (You could change the code of
sp_start_job, but it is hard to recommend doing that.)
You might be able to cobble together a workaround, something like this:
1. Create a job that runs as sysadmin which wakes up fairly frequently
(every 5 minutes?) and checks for some sort of flag. If the flag (a row in
a table / a file on disk / etc) is present, this job issues the sp_start_job
for your DTS task and removes the flag.
2. Create a stored procedure that allows your trusted person to set the