I was sold a 43mm BLS Navitimer recently even after being told it was a 46mm. After I complained to the dealer I bought it from they contacted BLS and BLS said that they no longer make any 46mm Navitimers. So to answer your question, it would seem that only 43mm is available now. I was super bummed as I have a large wrist as well. the 43mm looks a tad too small.
Most reputable dealers I contacted said they cannot get 46mm. However, I've spoken to some no name random instagram dealers and they are convinced they can get 46mm. You'll either end up in the same situation as me or you'll end up getting a very subpar rep from an unknown factory. BLS seems to be the only game in town ATM.