Hi @peter1942
I have been using a Swisscom LAN cable (yellow caps, white cable) for years to power one of my desktop-switches. It works like a charm 😉.
Just note that the Internetbox cannot provide PoE, so you will have to either use a PoE Injector or a PoE Switch to power the AP.
Keep in mind that as it’s not outdoor rated, it will degrade due to the UV radiation from the sun - so you might have to replace it from time to time. (This, of course, highly depends on how/if it is exposed to the elements outside)
Best,
r00t