Humm, I would have thought these are a) rarer than hens teeth and b) firmly under the control of the Ad.Mech and its existance unlikely to be admitted to in any circumstance, even to the Inquisition.
Well, yes, newly discovered STCs are rare as hell, but they aren't immediately the property of the AdMech upon discovery. Sure, the STC will be as useful as a chocolate teapot without AdMech help, but the STC template itself doesn't necessarily 'belong' to the AdMech until it actually falls into their hands.
I reckon that the Baal Predator is a great example of this. The Blood Angels found the STC, and chose not to hand it over to the AdMech, keeping it for themselves. The Space Marines have their own tech-support people (techmarines) so they tend to get away with this sort of behaviour, even if there may be other negative consequences further down the line.
But people tend not to just be walking along the street and trip over an STC. People who find them, by and large, will have been looking for it. They're normally on uncharted worlds long forgotten by the Imperium, or are hidden in some god-forsaken place. So, your inquisitor will need a damned good reason to find one.
Whilst not impossible, such a story would take some careful crafting. Perhaps the Inquisitor was investigating a non-admech radical techno-worshipping-cult on some backwater planet, only to discover that their 'idol' or 'god' was actually a piece of technology far more advanced than any he had seen before. (Even an Inquisitor wouldn't know what an STC template looks like, in much the same way that an AdMech magos probably wouldn't know how to tell a bloodthirster apart from a lord of change.)
He might have taken such a piece of technology away on his pimp-freighter, deciding that it was probably too valuable to simply destroy or hand over to the planet's authorities.
Although how he got the template identified and put to use without the help of the Adeptus Mechanicus would probably need some explaining. It's a bit like when you're playing monopoly, and you've got Park Lane, and your friend has Mayfair. Neither of you can make use of those properties unless you hold both. Your Inquisitor holds the template, but lacks the expertise to use it, and the AdMech have the expertise, but not the template. And if the AdMech KNEW that you had a template that you weren't sharing, they would probably assassinate you and steal it. Entire wars have probably been fought over less.
A more reasonable explanation is that, as a dutiful servant of the Imperium, he handed the template over to an AdMech Magos whom he trusted. Upon discovering that the template was for a small ship, the Inqusitor became interested. Eventually, after much negotiation, it was agreed that the prototype model of this new ship should be given to the Inquisitor. The Inquisitor would use it in his day to day work, and the Adeptus Mechanicus techpriests on board would report back to the AdMech about how the ship held up.
So, basically, he would be doing product testing for the Admech. It's a bit more reasonable than "I found a template, used it, and ain't sharin'. Y'jelly?"
P.S. I was under the impression that building ships took centuries, not decades. After all, you're basically building a city in space. That sort of thing doesn't get done within a single lifetime... How long did it take to build London, or Chicago?