There is more than one way to do this - inevitably!! How you do it will depend on your budget.
1. You will need a wireless network card for each machine (PCI) and internet connection sharing enabled
2. Same equipment, but with a wireless modem / router that connects to one of the PCs via ethernet. This overcomes the need for the Pc with the BB connection to be on when you want the net on the other PC. Better, but more expensive. Also, have you got a spare slot in the SFF Mesh PC? If not, route 1. is necessary unless it also has a PCMCIA slot into which you could stick a wireless LAN card. Often come bundled with the modem/raouter/wireless access point.