If your boss isn't an IT guy, then you may be able to get his attention more by focusing on business risks. There are two big ones that your boss will need to consider if you're all wireless and...
You accept credit cards for payment
Congratulations! You're under PCI-DSS regulations from the credit card providers. There's a bunch of work that you will need to do satisfy the auditors that your card information is safe in a wireless environment.
You have health care information
Congratulations! You fall under HIPAA. I'm less familiar with this since my office is not in health care, but I do know you will have additional work to get auditors to sign off that your wireless is secure.
Even if you manage to meet the technical requirements, these business rules will likely drive your wireless off of your internal network. So you're going to end up either running a VPN from the wireless to get internal access, or you'll have to make all of your resources and apps run from a browser. And I'm not even touching on whether your boss would mind if someone could access something confidential to you. At least in a small office, someone would (hopefully!) notice if a random PC was plugged into your network.
To directly address his concern that cables are going to change, you should tally up how long Cat5e has been viable while wireless has gone form 802.11 b to g to n, with the a standard a bonus tech cul-de-sac. ;) Tally up the costs, and I think you'll find yourself way ahead with a wired backbone.