The hardest part about anything that's not atx or sfx standard psus is fitment. The only question is if it will physically fit in the space you have now, and still have airflow through the fan.
Otherwise it's the exact same 12v, 5v+,5vVsb, 3.3v rails etc. The pinout is meaningless. You can lookup, or just look at the 10pin connector, and swap it with some of the matching wires from the 20+4. They are the same thing, there's just more of them.
So the adapter is fine for that use, just don't get the cheapest one, I'd recommend you go with a better brand, they'll use higher grade pins, thicker gage wire etc. The cheapo's tend to cut corners.