Shooting fireworks out of a tip-up would be illegal unless it's a sparkler cone or fountain. Anything that leaves the ground or explodes isn't allowed. It would be easy to do something like that but unless you have a fireworks permit you wouldn't be able to use something like it.
A sled with a front ski that turns has been done and are pretty straightforward to make. Essentially all you'd be doing is adapting the front steering mechanism off of a radio flyer wagon and putting it on a sled. Not much in terms of developing engineering skills in an academic setting there.
If you plan on marketing anything you design and build the biggest factor to consider is establishing a price point. If I see an item for sale that I could use on the ice I will see if I can build my own at a fraction of the cost. Jaw Jackers are $40 a piece. In about 15 minutes I can build one for $4. I cranked out 30 of them in just a few hours in November....and they work just as well if not better than the original. This winter I've been using my own hole covers that have less than $1 worth of materials in them, they pack up and are transported easier than anything on the market, and they work a lot better. Very simple idea, nothing fancy at all, just a little bit of an understanding of thermodynamics involved.
Ice anglers are backyard inventors by necessity... some of us come up with some pretty wacky and unique creations. A good place to look for ideas or see if ideas have been pursued are the forums on iceshanty.com. Pages upon pages of homemade inventions are there.
But....back to the jaw jacker concept. We are now seeing more and more battery operated jigging mechanisms on tip-ups or on rod holders. What we don't see is a jaw jacker type contraption that incorporates a wind activated jigging device. Essentially you'd need to build a rod holder and trigger mechanism that is free to move with the wind without tripping the release....but still have flexibility built into it so you can use heavier baits, different rod actions, etc. It's something I've been kicking around all winter and is on my summer "to do" list. That seems like something a bit more suited for a high school project since it incorporates a whole bunch of design elements.