fork should be the way to do it.
E.g. you can detach normal command line scripts from the terminal and so let them run in the background by using:

fork && exit;

Because fork returns the child PID (>0) to the parent and 0 to the child it can be used as a boolean.
As similar code should work for you. Did you tried to set $SIG{CHLD} = 'IGNORE';?

AFIK exec replaces the perl interpreter process with the called command - that's not what you want.