Yes, it's perfectly fine. I know those spines will get ya'. I find using kitchen tongs to handle them works really well and a very sharp knife. Give the pups pots of their own and they'll grow on. Or you can create a nice display in using a wide shallow dish and colored sand. Make gift for somebody?

You can remove them if you wish but it will grow more as this kind of cactus just does this... Its a good idea to put the babies in a dry very sandy compost until they have some good roots. Don't be tempted to water them until the roots are well established.