-No communication would be face-to-face (Not sure if this is a penalty)
Renders Tailored Pheromones and Kinesics useless, pretty big deal.
How big is the floor/area the kidnappers and hostages in? Are they in multiple rooms? How many kidnappers? How many hostages?
The biggest job of the Face wouldn't be to get them to outright release all hostages, but to just improve the situation. Release
some hostages (women and children), build good will (get them water, food, smokes, etc.), be a distraction, mitigate anger when the Spirit is nuked or other counter-measures are taken, and of course, depending on what the hostage-takers want, negotiating those terms, i.e. buying time. During that time, the Caster and Hacker should be doing recon on the building, he'd probably even be given Admin access to the system if asked. After all the ground that could be made there was used up, It'd be worth trying a hostage-swap thing, dress-up a couple well-chosen Runners (Awakened, Hand-to-Hand guy, cyber-gun guy, etc.) as "every-day people" if possible, pose them as high-value members (CEOs, etc.) of the organization which is being victimized; "they'll get you results" "they feel they are the ones who deserve to be the object of your anger, don't want their people to suffer" or whatever spiel might appeal most to the motives of the villains. Whether or not that works, the Hacker should be able to silence the alarmed doors and disarm the explosives if they're triggered wirelessly, after that send in a precision extraction team (stealthy with silent weapons) which in combination with the inside men would be the best bet, this would all be preferable to a coordinated lights-out/gas grenade/flash-bang/spirit summoning/snipe any exposed hostiles attack, IMO.