Li-ion batteries usually follows the naming convention according to size, so for example an 18650 battery is 18 mm in diameter and 65 mm in length. 0 denotes cylindrical form.
In the past, a tailing 5 wound indicate a prismatic cell but yours doesn't.
Anyhow, my best educated guess is that 35 denotes the length, 08 the width and 3 the thickness and all ...
You could make a custom charger BUT I'd strongly recommend against it.
The energy difference between 4.2 & 4.4V will be small and you will get useful whole of life capacity improvement by using 4.2V end of charge.
You can test this by
CAREFULLY manually charging to 4.4V with a power supply set to 4.4V and current limited to Imax,
then letting the ...