Sounds like a weak argument. They're not going to be inclined to operate a local ML system just for one or two people.
I would see if you can get a quote for locally-hosted transcription software you can run on your own, like Dragon Medical. Maybe reach out to your IT department to see if they already have a working relationship with Nuance for that software. If they're willing to get you started, you can probably just use that for dictation and nobody will notice or care.
https://en.wikipedia.org/wiki/Tay_(chatbot)