I was a little bit premature in my assumption that you can’t delete SIM contacts in customized Android dialer.
It turns out in iPhone copies and other phones with highly customized Android interface, the common three dot’s menu at the top right corner of the screen can be accessed by holding the home button. As you can see the menu even has a separate item – Delete SIM1 Contact. Probably if the phone was equipped with dual SIM cards, there would also be a option to delete contacts from SIM2. Select the item, and the contact list will now show only SIM card entries. You can delete them one by one or in bulk, and they will never appear in the contacts book again. So you can uninstall the now useless COPY 2 SIM CARD app, and you certainly don’t need SIM adapters that should’ve enabled you to insert your new micro or nano SIM card to an older phone only to clear contacts from the card.