Hi Bumble!  Interesting question!  May I ask, first of all – why do you think it might be a Hans Holbein sketch in the first place?

Oh, ok.  I think there are a variety of ways to trace the origin of such as sketch, and using stylistic analysis like you're doing is one way…but I think it is limited in value without further evidence.  Looking at a few Holbein works briefly, it does appear that Holbein liked to do portraits in 3/4 view, including the Meyer Madonna (notice the cloth wrapped around the chin of the woman in the background, similar to your sketch).  Also, if we look at two sketches done by Holbein – Portrait of Lady Elyot and Portrait of Sir Thomas Elyot – we can notice a number of similarities (eyes, lips, eyebrows, etc.).  There are some differences as well (the Holbein sketches don't pay as great attention to the clothing details as the artist did in your sketch).  Also, you can notice how Holbein wrote the names of the subjects of his portraits directly into his sketches, though your sketch doesn't seem to have that (at least not in the same location as the other Holbein sketches).In the end, without knowing more it is difficult to know whether your sketch is a Holbein, a sketch done by someone who trained under Holbein or Holbein's school, or a copy done of a Holbein work just last year (or none of the above).  One question I would ask about your sketch is how a Holbein work could have aged so well, particularly given the fact that it was handed down within a family rather than, say, kept under the watch of a museum (paper usually develops some discoloration over time....though not always).  So, if you can find other textual information on the work itself (e.g. in the area where the work is covered by the mat or frame, or on the backside) it may go a long way to helping to uncover the identity of the artist.

Glad to be of assistance.  I should add that if it is a Holbein, and if it wasn't signed or contained a name of the subject written on it, it could mean that it was used as a study for a further work (i.e. painting).  There may be a Holbein work out there somewhere that was based on your sketch, and someone who is more familiar with Holbein's complete works could possibly make an I.D.  If you want, I can try to give you the name/names of people who could potentially help you.  Also, I'm guessing there might be a catalog of Holbein works available somewhere, and your sketch may be listed in such a catalog.  If so, it would be easier to make an I.D.  If, on the other hand, you have a work of Holbein's that was previously unknown, you would likely have an even rarer (and more surprising) work on your hands which would be rather helpful to art historians...I'm sure a Holbein specialist would offer to help you out in finding information you are searching for.

Bumble, I sent you a pm…don't know if you checked it yet.