No phones, period. The phone will still send out signals, just that it won’t be allowed service onto networks without the SIM card. They can still trace the phone to the point it turned on and since you used it previously as a personal phone there’s probably records they can pull on it from your carrier at the time. They can probably trace it to you via the various numbers tied specifically to that phone. As much of a PITA it is, getting a small digital camera is the way to go as long as it doesn’t do any connectivity. Just be sure to scrub the meta data on all pictures if you share them or post them online.