Withdraw cash from banks without ATM fees

Do you mean using your local visa card at an atm to get cedis? If so as long as you use the atm of the bank issuing the card then I withdraw cash at Standard Charter and Ecobank without fees

if you mean the VISA card of a non-Ghanaian bank (e.g. my bank in Germany - ING) the only one I've found so far is Republic Bank (formerly hfc bank). I can vouch for the branch at Tantri, Cape Coast, corner Sarbah and Tantri Roads.

What Bank wires money from the US to any Ghana bank?

Michael,
the following may be off the mark and only applies if you already have money on a bank account outside Ghana:
I guess just about any bank will wire money to Ghana, at least the reputable ones, Wells Fargo, Barclays and suchlike.
However, I find that the banks are even more expensive than Western Union, although WU are pretty expensive. If you go through the WU legitimisation process before you leave the States (postal communication <> Ghana is beyond slow) you can then transfer to yourself online from your own computer (assuming you have internet access to your account in the States).
In my experience the "cheapest" way to get your hands on your "foreign" money is to withdraw cedis from one of the Ghanaian banks mentioned here, using your VISA card or Mastercard.
Of course that is no use for large amounts.
HTH Rod