As I'm watching it, it seems the perfect movie to riff on. Basil Rathbone's hair - especially in the first 10 min - is completely ridiculous (couldn't find a picture unfortunately), as is the dialogue, the characters are very British - which is always fun, and many scenes feel out of place and are already laughable. Plus with the new Sherlock Holmes movie coming out, the timing seems appropriate. The runtime is just over an hour.
Come to think of it, I haven't seen it, but they could probably just riff the new one.