The battery tray of the 436HP is designed to accept 1.2-1.5V alkaline or rechargeable NiMH AA batteries. It is wired in series to produce nominally 3.6V to 4.5V. The charging system in the 436 is “dumb” in that it’s based purely on time and is not adjustable, neither manually nor automatically, so for the best performance and life of standard rechargeable batteries most people recommend avoiding charging in the radio and instead using an inexpensive external smart charger.
Many Li-ion cells the size and shape of AA are ~3.7V, so without opening the radio up and permanently modifying the battery tray to convert it to run in parallel, they will NOT work to just drop them into the battery tray (11.1V), and the charging system in the radio doesn’t know how to handle them. If you have an external charger and find some sort of Li-ion ~1.5V AA replacement cells, they should work as long as you remember to not charge them in the radio. I don’t know if such cells exist off the top of my head, but with the proliferation of no-name battery products out there maybe they exist. Even if they do, YMMV in regards to quality, safety, and capacity ratings.
The easiest way to use Li-ion power is to get a standard 5V USB battery pack, power bank, whatever you want to call it, and plug in a cable from it to the radio’s Mini-USB port. Same as getting 5V power from a wall-plug phone charger or mobile 12V socket to USB phone charger, except the power supplied should be cleaner assuming it’s at least an OK quality unit. A compact 10000mAh pack would in theory provide power for massively longer than the popular 2000mAh NiMH rechargeable AA batteries and costs about the same as an external charger (if you don’t already have an external charger and a bunch of NiMH AA batteries laying around). And of course if you wanted to you could bump it up to way more, like a larger 26.8Ah pack (over 13x the battery life of rechargeable AAs on a single charge). But any sort of external battery pack then calls into question how truly portable it is for a handheld scanner. You might be able to use something like 3M Dual Lock to secure the battery pack to the back of the 436, if that floats your boat. All depends on how portable it needs to be and how long you really need the battery life to last per charge.
Lastly you have options like the Energizer Ultimate Lithium batteries, relatively expensive and non-rechargeable, and in AA form they appear to be approximately 3500mAh. Probably not a cost effective option.
EDIT: Here’s a good example of a 10Ah Li-ion battery pack if you decide you want to go that route: Anker PowerCore 10000