I think your best bet is to be honest and tell them. If you are honest now then they may well accept that you have changed - especially if the offences were petty and a long time ago. However, if they find that you have not been honest about your past then they will have every right to think that you are still essentially the same.
There are lots of checks on people now and your chances of any lie remaining undetected are not high. It's also a small world and there is a chance that someone will come in the shop one day, recognise you, and spill the beans to your employer. You would have committed a sackable offence. Even if no one does spill the beans, you will always live in fear that someone will. However, if your employer knows your past, then you will have no worries at all.