The only way to do exactly as you request would be via another BB...restore from BB Protect, and then copy (one by one) your contacts from that BB to the SIM. BB Protect backups can only be used to restore to a BB...there is no other usage of that method of backup.
The Desktop Software, on the other hand, offers more robust access to your data. For instance, you can obtain a PC-based 3rd party BBB/IPD parsing app. Further, with Desktop Software prior to 7.0, you can export your contacts to CSV on your PC.
In any event, if all you have is BB Protect backup, then there only solution is as I've said above.
Occam's Razor nearly always applies when troubleshooting technology issues!
If anyone has been helpful to you, please show your appreciation by clicking the button inside of their post. Please click here and read, along with the threads to which it links, for helpful information to guide you as you proceed. I always recommend that you treat your BlackBerry like any other computing device, including using a regular backup schedule...click here for an article with instructions.