In any removal operation, you have to decide what is most important to preserve.

Sometimes it's the board, sometimes the device, sometimes both.

Snipping the leads is perfectly valid, and probably the least stress to the PCB.
DIP heaters are another way to go, but of course you need a different
one for each package.
I use a pace micro for this, one lead at a time. If the PCB was
properly designed, the chips just fall out.  But, if you don't
maintain your pace, it will perform badly.
If you can't wick the holes clean, that's telling me that the PCB
design is a factor. Too small of a hole, or no thermal relief, and
there you are.
It's not always easy.
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