I don't know about MAKO lights but many of my lights will take either a rechargeable lithium 18650 OR you can use a plastic insert which holds 3xAAA alkaline batteries. Most of the Chinese eBay lights I've got work this way as do my dive-rite bx-1 lights. The dive-rites are not as bright as my other lights but I use them most often. They're bright enough and they're small n sturdy. I think dive-rite has discontinued the bx-1 and released a
bx-2 that is brighter (just over 1000 lumen) and appears to use 18650. I can't say for sure if it comes with the insert that allows you to use 3xAAA in place of the 18650.
Although the lights take rechargeable (as does any light that will accept AAA or AA batts), I also insist on a light that will run on disposable alkaline. I made that decision not long after getting certified when I couldn't use my rechargeable can light one day because I'd forgotten to charge it. You can buy aaa alkaline batts pretty much anywhere in the world if needed.
1000 Lumen Dive Light This light is nice and bright, but it takes 3 "C" batts instead of AA/AAA so it's a little bigger. You can buy a similar model at Sunshine Scuba in largo if you prefer to go local. I think Sunshine charges a little more.