It's not the INT signal you need to worry about, but the HUP signal. This can also be averted by disassociating the new process from the old one (which also disassociates it from the controlling terminal, preventing things like the HUP broadcast from reaching it) by using
POSIX's setsid function. I believe perlipc gives a good example of a "daemonize" function that does a good job of setting up a child process in such a way that it is completely disassociated from its parent.