The name Wi-Fi never was an abbreviation of "wireless fidelity".
Therefore I see two approaches to naming it in Latin:
Use Wi-Fi as a name.
Express the idea "wireless network access" somehow.
In the first approach the name would be indeclinable, so there is no case inflection.
Cases can be expressed by an auxiliary word (possimne uti Wi-Fi tuo?) or the ...
To me, wifi feels like a word that the Romans would have just borrowed rather than used their own phrase for. If you swap out the W for a V and treat it like a third declension noun, you get vifis as the genitive noun. I'm not sure how awkward that would sound to those more experienced than me, though. I suppose it's better than vaefae, though. :)
The Roman aqueduct is considered one of the greatest inventions of the ancient world. Commenting on this technology, Cicero had the following to say:
Adde ductus aquarum, derivationes fluminum, agrorum irrigationes,
moles oppositas fluctibus, portus manu factos, quae unde sine hominum
opere habere possemus? Ex quibus multisque aliis perspicuum est, ...
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The above is in unicode, not beta code. But also note that there are a few betacode to unicode translators available.