Dealing with an airport update error (time machine/MacBook question)

My Macbook is giving me messages that it is not doing time machine updates anymore. I’m not particularly computer-savvy, but I was able to trouble shoot a little, and what I eventually got to was “airport update error -6727.” It seems (if this is correct) that there is an update to the time machine that I need to install so it will work again.

However, it doesn’t work when I try to do the update. Uncle Google led me to an Apple support page that said you can’t do the update wirelessly - you have to connect your Mac to the time machine with an ethernet cable.

Alas, there is no ethernet port on the Macbook. Yet more pestering of Uncle Google found that you can apparently buy an adaptor.

I’m willing to try that, but I don’t want to waste time and money on something that is barking up the wrong tree. Howzabout it, smart Dopers? Should I invest in the ethernet adaptor?
.

Depending on how convenient it is, you might want to make an appointment at a local Apple store and have them do this for you. You also might contact a local user’s group, and have one of their members do it for you.

A Thunderbolt to Ethernet converter is a useful, but pricy adapter.