Megz - Are you currently a green card holder? If you are, chances are this will only be an issue when you apply for naturalization or if you renew your gc or if you apply for a reentry permit or if you apply for anything that requires biometrics. When you apply for the benefits listed above, you will need to divulge all arrests and this is notwithstanding the fact that you have not been fingerprinted for the shoplifting. lying is extremely risky as that's fraud and that could be a reason to exclude you from the US. Now, I really don't know what will happen when you travel - chances are, US VISIT will not flag you for additional questioning as you don't have an arrest record but you never know.
And if you not a gc holder, I would, if I were you, divulge this arrest when you apply for your GC. Because you have not been arrested, you might be able to get away if you don't divulge the arrest but that's very risky. Again, fraud will get you excluded from the US. I don't know what your arrest was for, and what the penalties are, but you may qualify for the petty offense exception and won't need any waivers...otherwise you would need a waiver...but talk to a lawyer about waivers.
Basically you have a choice. Because you were not finger printed, it is very unlikely that the NCIC database and other criminal databases will contain a record of your arrest - as such, you might be able to not divulge this arrest when you apply for immigration benefits as it is extremely unlikely that USCIS will come to know about your arrest; you will only have an arrest record if you are fingerprinted and photographed at the police station, and all records, whether it is state, local or county will be shared with the FBI who maintains the NCIC. BUT, there is always the possibility, however remote, that USCIS will discover this arrest and will initiate removal proceedings should you chose to lie about it. So, the question is whether you wanna risk it...is the risk worth the reward.
Good luck