Can you power a camera flash with an external Li-Ion battery?

I have 2 external camera flashes. Both take 4xAA conventional batteries or NiMH cells.

After a short while the flash does not like the NiMH cells anymore and I need to replace them because of wear.
I also do have a bunch of Li-Ion batteries as 18650 or pouch cells. So can they be used instead?

Theory

Let's start with a the theory. Fully charged NiMH cells have a voltage of 1.2V times 4 makes 4.8V, new one-time batteries have 1.5V so 6 in total.
5V is right in the area and there are many cheap modules that can transform the ~3.7V to 5V powering USB devices.
So I need to make an adapter to simulate the AA form factor with wires going to such a module + battery pack.
A little CAD time later:
A dummy battery where you can attach wires to one or both end and easy to print with common 3D-printers.

There is a small hole from the side to the top or bottom so you can pass your wire through, remove the isolation and let it stick out at the end (optionally put the remaining wire back into the other hole.

The battery charger and 5V module is a generic module, nothing fancy.

Real world

The 3D print worked, AA-dummy connected to the charger module and the charger module connected to a fully loaded battery pack.
Switching the flash and: nothing.
Checking the output voltage and 4.2V. I was under the wrong impression that the module contained a step-up function, but doesn't and the 4.2V from the Li-Ion battery was not enough.

So, let's connect the dummy batteries to an adjustable power supply and check what works.

I set the power supply to 5V 2A, this what a typical power bank or step-up would supply.
The flash turns on and shows the boot logo, good thing. But after a few seconds: A power low indicator. Turning off and on worked but the flash was drawing the limited 2A and the power supply was cutting down the voltage, as intended.
So the power source needs to supply at least 2A, which explains why the batteries are so short living (until empty, but also how often they can cycle).
Triggering a flash at full power takes about 15 seconds at 2 Amps to fully recharge, wow.
But the power supply can do more, so raising to 3A: maximized, 4A: maximized, 6A: still maximized out. Of course, a way shorter time to recharge the flash. This is the limit I'm comfortable for testing, I don't want to destroy anything. Looks like there is no form of current limiting and the electronics seems to rely on internal battery resistance: that's unfortunate.

So some quick math: would a resistor in series work and what size does it need?
Assuming I want to limit the current to 2A, the max my step-up converter is rated at and 5V output voltage it would be R=5V/2A or 2.5 Ohm and power loss P = U*I 5V*2A=10W hmm, I don't think I have such a resistor. And I'm not sure if a typical 0.25 W resistor would survive that, even for a few seconds.
But I have a few 4.7 Ohm 1/8W resistors that I can test with...
OK, with the 4.7 Ohm resistance the current should max out at I = U/R so 5V/4.7 Ohm or ~ 1A and Power loss ~5,3W, only a bit more than 1/8W. I'm willing to try that :)
So power supply set to 5V, max 2 Amps, the resistor in series and powering on. The flash turns on, power draw is about 0,5A but before the the flash tells charged and ready the resistor starts to smoke. So I quickly turned it off without firing the flash once. Now I have a resistor that turned a bit more greenish instead of previously blue.

So in theory this works.

Summary

So while it might work with 5V input (power pack or 5V from socket), you need some electronics to limit the current (by reducing the voltage), putting a resistor in line would generate a lot of waste heat.

I'm sure there are cheap current limiting step-up-converters out there, but for me it isn't worth it and I'll buy a new set of AA NiMH batteries ;)
Or some time in the future a new flash with an internal Li-Ion battery or at least some current limiting built in.

But in the end, it was worth a try and maybe it saves the life of some electronics if you read this first ;)

And maybe my next project works again.