How bad would a secured wireless connection be if the client doesn't have the budget for wired re-work?

I have a new client who runs an assisted living campus. When they had all the networking set up originally(by someone else back then), everything was made wireless. They have zero wired connections. To double down on that, believe it or not, everything(work computers with resident information, etc) is on this network and the network is unsecured! I want to get them locked down and I'm putting together a proposal to rework the wireless network, making it secured this time, and to have all of the office computers wired. In the event the cost to do this(much of which will be the contractor routing the cabling) is more then they want to spend, would it be absolute taboo to have the office computers connected via secure wifi? First off, I know they should be willing to spend whatever necessary to secure their resident's data, but this is a hypothetical. I got to thinking about this and while I'm not a fan of wireless networking at all really, what about hospitals? I'm pretty sure all those laptops on carts they go from patient to patient, room to room with, aren't plugging in to an eth port each time - and that's pretty sensitive data.

What would you do if this were your client?