One generally does not need a replacement for a specific chip, but a few of those chip's features only. So you are looking for a switched constant current source of how many amps and for how many volts?
Do you recommend doing a one by one pin soldering using a small pointy tip.. or doing like the video using a flat/diagonal cut tip ?
I would say I have a decent 40W soldering iron with temp control and a pointy tip.
I usually use soldering paste, it seems liquid is more manageable for this operation.
To remove solder between pins, you can use solder wick. Solder wick is composed of small copper strands braided together with some chemical additives that have been formulated and manufactured in such a way to attract the solder. Basically, you're playing with surface tension.