Is there a way I can turn off the immobilizer system with the unlock key in the door?

No. The emergency key only unlocks the doors. Without the transponder chip the immobilizer cannot be turned off. A mobile locksmith can replace the keys and erase the old ones, so they won't be a liability. A dealer can as well but a smith is usually cheaper.
This is the method used.

1. Turn the ignition on (transmission in park/neutral).
2. Use the DRBIII and select THEFT ALARM, SKIM, then MISCELLANEOUS.
3. Select PROGRAM IGNITION KEYS.
4. Enter secured access mode by entering the vehicle four-digit PIN.
Follow the on tool instructions to program the keys into the system.