Using a graphics tablet to support recorded lectures?

My lectures (mathematics) are delivered in a theatre with full projection facilities, and my lectures are given as PDF slides. But I often need to explain something not covered in enough detail on a slide, in response to a particular student difficulty (my lectures are very interactive!). For that I can use the whiteboard in the same room.

However, my lectures are recorded, and the recording system only picks up, as its video, what's projected through the computer onto the projection screen. My whiteboard ramblings (which often amount to a significant part of each lecture) aren't recorded, although my voice is.

A simple solution would be a graphics tablet which I could switch to and write on; as it would be projected through the computer system it would be recorded.

So - does anybody have any advice for a relatively inexpensive graphics tablet which would work for this purpose?

(A few years ago I used a Lenovo Thinkpad Tablet, running Android, which came with a nice digitizer pen. But my newer Lenovo Yoga tablet doesn't support such pens. And I don't want to buy a new whizz-bang tablet+pen. A cheap-and-cheerful solution is my hope here!)