Broadcast and Blu-ray HD is always 16:9, which is why movies with other aspect ratios are either pillarboxed or letterboxed to form a complete 16:9 frame with black borders if needed.
Whether HDMI by itself can transport anything other than 16:9, I think yes, it can, after all my computer monitor is 16:10 and is connected over HDMI. But I think that consumer-grade devices will fit everything into 16:9 frame.
The
digitizing box that I have has two explicit settings, for 4:3 and 16:9 source. If I select 4:3, it pillarboxes it into 16:9 frame, so the output is always 16:9. It seems that this is the result that you want.
12voltvids claims that
his box, which is very similar to mine, but newer, outputs 4:3 as native 4:3 HD, which should be 1440x1080 with square pixels. Some of these boxes scale everything into 16:9, so if you have 4:3 source frame, it will be stretched to fill the screen, ugh.
Three fixed resolutions of these boxes, 1280x720, 1920x1080 and 1366x768 hint that they probably use hardware from decade-old TV sets. My plasma TV has native resolution of 1366x768.