I have been trying to work out how my now-death knight draenei might have gotten himself into the situation he is in. Here is what I have conjectured so far:
Previously, he was a jewelry maker with some relatively minor military experience on Draenor, mostly of the "Here, hold this axe and protect the settlement" variety -- not exactly formal training. After the Exodar crashed on Azeroth, he took up his trade again and that was pretty much it, though he did get asked to assist with teaching some of the draenei's new allies some of the techniques they had brought with them. Either way, he didn't really get involved very much with the events of the Burning Crusade.
However, when the Scourge reared its nefarious head, he felt called to sign up for the expedition to Northrend. As his unit was traversing the Dragonblight on the way to support the 7th Legion at Wintergarde Keep, they were overtaken and most of them killed. His body was scooped up and resurrected, etc. etc.
Now, the real question is: Was there enough time for him to be part of the Acherus death knights and be freed at the Battle for Light's Hope? As best as I have been able to determine, the answer would have been "no," since the Battle for Light's Hope took place before the first Alliance ship set said for Northrend at all, so unless he had reason to have been on the continent beforehand, no dice.
The other question is, did the Lich King then (presumably) continue raising death knights? With all these Alliance heroes streaming into his backyard, and given the Converted Heroes wandering around in Icecrown, I don't see why not. If this is what happened to Shaatnez, though, then when would he have been freed from the Lich King's hold? My thought was upon Arthas' death.
I was thinking that he was probably being trained in Naxxramas, then sent out on missions through Icecrown, and broke free in the brief period between when Arthas died and Bolvar took up the mantle.