The problem is that the single cell protected batteries are a lot less than 9V. They are 3.7 nominal/4.2 max for the average Li-Ion battery. Malkoff does make 30/31 series droppins that are better suited to single cell usage. Now I believe from the past the drop-in will work for a while on a single cell, but I can't remember the details right now, and I can't put my hands on an M61WL right now, I may not even have that one. That said in the past some people liked this dropin with a single cell because it dimmed when the battery got lower since it was running in unregulated mode with the lower voltage.
An 16650 Battery would be a good one to try and see if it works for you, or see if you can find someone who has already tried that combination. Hopefully someone will be able to help you with this combination. There should be lots of information on the main LED forum about this I would think.