You can just remove the pups and plant right away. If they are low on the plant and between leaves you can pull the leaf below the shoot way down and then carefully remove it trying not to break it or it will ruin it. Ive ruined many being impatient removing the ones between long leaves. The ones in the dirt just pull it strait out at the roots.
Ive started removing some types feom my collection. The leaves are too spiney or the fruit are too small or they cant handle the weather here etc. Pretty much all the victoria/queen ones Im ditching and probably the red spanish and chees pines too.
The current best ones are the white jade, white sugar loaf, Paun, giant md2, tropical gold, maui sweet, smooth cayanes. The josepine is ok but the plant is pretty weak and the fruit are small and the plant seems to be a scale magnet. Some types clearly attract more scale than others. The sharp queen types are such a pain to work with and the fruit is very bumpy and smaller and tend to have a lot of waste from the peel.