It would make a lot more sense to take your unfiltered and undiplomatic private conversation to a nearby private establishment. If you are remote and can not do this I would simply use a not supplied by work phone. This is for your protection and whoever you bring along to vent. There have been at least two occurrences in my career which have forced my hand on employee communication and in both cases, a blanket refusal was not an option. If you don't want to say something publically don't assume anything your company pays for is private until our society changes its views on where the expectation of privacy exists.
