So, this is an idea that should totally be supported, but let me step back a moment to hi-light some of the landmines it hides, which may give some insight into why the gadget rules are constructed as they are.
So, a Universal skill is a skill that can be used in virtually any situations. In games where magic is very flexible, it can often turn into a universal skill, making all other skills (and characters who have invested in them) less viable. Gadgeteering runs this risk, but is usually curtailed by the limits of how many gadgets one can reasonably carry around. Jury-rigging, however, dispenses with that limitation (at least conceptually). It creates the danger that the character can come up with some improvised device to deal with any challenge that comes up.
That's unsatisfying for a couple of reasons. First, as noted, it hoses other skills, and can really flatten the game. Second, that's not how it's supposed to go. If you watch MacGyver or see other characters of that sort, they do this _occaisionally_, but it's just part of their overall capability.
Now, to this end, I think the solution that it just be used as a different flavor of universal gadget is the simplest and easiest to implement, so I'm all for that. But That may be a bit to _much_ capability for some characters. Specifically, they may want more width (usable in more situations) and less depth (they don't want potent outcomes).
So, to chart a path between these, i would look at what purpose these improvisations serve. Sometimes it is to solve a specific problem, but I'll tell you something - that's pretty boring in play. It invites little creativity or investment when it's just a matter of whipping out your problem solving device (this same problem applies to universal gadget, so some of this advice applies there as well).
Where these improvisations get interesting is where they change the situation. When in a locked room, an improvised lockpick doesn't open the door itself, instead it creates an opportunity to roll where none previously existed. *That* is much more powerful, because in letting the tinkerer be cool, it creates another opportunity for coolness, either for the tinker, or for the person things are handed off to.
So with that in mind, I propose the following trapping and stunt pair:
Trapping: Right Tool For The Job
The engineer knows that you get things done with what you've got. When the character is faced with a challenge (something calling for a specific difficulty to beat) and he has the means (notably time and resources) he may attempt to create a tool for this specific problem (or type of problems). To do so, the character rolls his engineering against the difficulty of the challenge and, if successful, tags it with the "Right tool for the job" aspect. The character must describe the tool and how it's going to work, and the GM may increase difficulty if this seems like a mismatch of efforts.
Assuming success, the aspect may be tagged to change the skill needed to overcome the challenge to one described when the aspect is set up. There is one important limitation to this tag - the engineer himself may not tag it for free - only other characters may do so.
Using this trapping assumes a base time of a few hours. This can be reduced by the Grease Monkey and Mister Fix It stunts.
For Example: Jet Black needs to drop the Chronobomb down exactly the right air shaft to disable the Eternal Fortress, a task of superb athletic difficulty. Sadly, he was never much of a footballer, so he hands the bomb to Sally Slick, who takes it into her shop and modifies up an old flare gun. She makes her roll and tags the aspect on the problem (in this case, the vent) so that Jet may now make the roll with guns, rather than athletics.
(Jet actually has great athletics, but roll with it, it's an example!).
Stunt: Duct Tape and Bailing Wire
The character needs only the most minimal of requirements to use the Right Tool For The Job trapping. This generally demands a more colorful explanation of how exactly two paper clips, a rubber band and a tube sock will be used to create a gas mask or the like, but the player has a lot of leeway, so long as it sounds good.
The character can also work faster, reducing the time required for the effort by 3 shifts (dropping it from a few hours to a 15 minutes, cumulative with other stunts). However, when the character takes advantage of this enhanced speed, the situation also gains the aspect "Unreliable", which the GM is free to tag to add a complication. This complication should not directly make the challenge at hand harder, instead, it should introduce some level of unintended consequence to reflect the ad hoc manner of the solution.
PS - Though I'd probably then add another stunt: World of SCIENCE, which allows the use of the Right Tool For the Job trapping with science rather than engineering. Or do something like that.