Hi Kilokey. The only reasons I can come up with why they wouldn't work is if the charger terminals wouldnt touch both ends. Those 10440 are 10millimeters diameter and 44mm long. The cr123a that are listed as known functional are ~35 mm long, so the ends would touch both connectors........ No problem.... The other thing to know is charge current, The 300mAh batteries should probably be avoided due to the 500mAh of charge current(from the charger) This amount of charge current could cause problems with a battery that size. One of the most dangerous things that can be done with a lithium based battery is to charge it at too high of a rate. Over charging a battery(or charging too fast) can cause thermal runaway(expansion/venting/fire)..... For this reason I would stick to a higher mAh battery than the charger provides, for this instance that would be the 600mAh batteries. Just make sure you dont leave them on the charger much past when the charger goes from red(charging) to green(complete)......
Enjoy your new device. Stay safe. Happy
vaping.