Here are some synonyms that capture the same idea:
* Secretly
* Covertly
* Clandestinely
* Furtively
* Discreetly
* Under the radar
Example: The cat stealthily crept towards the bird feeder, hoping to catch a tasty snack.
The word "stealth" itself refers to the ability to move or operate without being detected. So, "stealthily" describes an action that is characterized by this ability.