Do you have an ice maker? That's a common ice maker sound (and can be normal).
Your defrost timer is more likely to be in the fridge compartment or under the lower kickplate than in the freezer compartment. (No particular technical reason; just the way it seems to be done.)
You can check the operation of your defrost timer before replacing. Google / youtube search your specific model number (often found on a sticker on the door). In general, the timer will serve to cycle between (most commonly) energizing the refrigeration circuit and (less commonly, typically on a 15-ish minute cycle) energizing the defrost thermostat and heater. The defrost thermostat then ensures that the heater doesn't excessively heat the freezer area, but rather just enough to defrost the coils in the 15 minute cycle.
If you have the timer in your hand (not connected to the fridge) and want to test it:
1. Check for continuity across two of the terminals.
2. Turn the timer until you hear a click.
3. Verify that you no longer have continuity across those two and instead have continuity across two other ones.
4. Turn it more until you hear another click.
5. Make sure it's like in step 1.
Then, if you want, you can make a jumper wire that will simulate the "refrigeration on" setting on the timer and run the fridge. If the noise goes away, it was probably the timer. If the noise remains, it's obviously not the timer... ;)
There is no real risk of damage to the fridge, but the timer does control power to the refrigeration and to the defrosting, so it can "break" the function of the fridge (until you replace it with a good part). In general, I've had excellent results from buying whatever part is cheapest, searching by part number. Many fridge parts are very common across many lines and model numbers.
Edit: Sorry, I originally read that the noise was in the freezer compartment. So, ignore the bit about the location advice; you obviously know where the timer is...