I don't think it will be I and II HD.
Actually, I think that making HD remakes would be more expensive and difficult than making Shenmue III. With a remake, they'd have to do loads of extra checks to ensure that everything is the same (even the smallest little events) and with games as large and expansive as Shenmue I and II it will be a very tricky task. I'd also imagine that they'd want to re-dub things as I doubt it would even pass for 'so-bad-it's-good' by today's standards.
With Shenmue III, there is a clean slate to work with.
HD ports on the other hand are viable, but we need to ask ourselves if we really want that and if it will make a good impression of the franchise.