There are two aspects to this issue.
One is security to the computer and router. With properly configured firewalls and such those should be as safe as they are going to be regardless of whether you hook in via CAT5 (hardwire) or wi-fi. THere is no real difference there.
The other is the unsecure wifi. While any data transmitted to/from a secure (HTTPS) connection is inherently encrypted and thus far safer than normal (HTTP, no S) traffic, wifi allows for a “man in the middle” attack to intercept the signal between your PC and the router; something that cannot happen with a wired connection (unless we want to get into TEMPEST gear which is far less common than packet-sniffing “war-drivers”). Using wifi is inherently less safe for that reason, even on a “secure” connection.
Then again, if you are paying with a credit card, your bank likely has certain fraud protections to limit/eliminate your losses in the event that you ARE hacked.
Also bear in mind that handing your plastic to a waitress is also quite risky ;)