But also remember that the strings are designed to run off batteries and those drop as they discharge. Rechargeables less so than alkalines (or the ancient zinc-chloride ones).
So the strings will run OK for a span of voltage. I run a few 3x AA ones straight off LiIon 18650's (not constantly on) which are about 3.7V for most of the cycle - when I start noticing the LEDs getting dimmer it's time to recharge) .
Slightly less bright than with fresh alkalines, but brighter than the alkalines in the later part of their life.

Nice thing is that with With either an adjustable buck converter, as well as resistors, you can tweak how bright you want the string.