SIM unlocking on a Verizon iPhone 4S is only for "global roaming" bands, or the GSM 900/1800 bands. So basically, if you went to Europe, you'd be able to pop in a SIM card from a local provider in say France. SIM unlocking does not apply to the GSM 850/1900 bands used in the United States, so no taking the thing to any sort of MVNO like Airvoice.
There might be ways around this, but they are highly technical and technically illegal thanks to the DMCA.
Your best bet is to order a new SIM card for Airvoice and migrate your current account to the new SIM card to keep using your old phone. Most micro SIM to mini SIM adapters can damage the contact points for the SIM card in a lot of phones, though they do exist. Noosy makes the best ones on the market.
It's that or you try to find someone who has a proper carrier unlocked AT&T or T-Mobile GSM 4S that you can trade for with your Verizon device. Or you could switch to Page Plus if you're that hard up for your Apple fix, they're activating the things now.