No other alternative possible that's still practical? Like stock placed in shoulder instead of armpit (like modern day rocket launcher)? Or the different trigger mechanism?
Sure, you can tweak things here and there. A button rather than a switch, and so on.
Remember that the bang-stick has a recoil. Newton's 3rd Law tells us that if the bang-stick throws a lump of metal out in one direction, the bang-stick will be pushed back in the other. If the bang-stick is going to be effective, then this recoil will be significant. If the person holding the bang-stick can't hold it steady against the recoil, then by the time the metal reaches the end of the tube, that tube is going to be pointed God knows where, and the lump of metal will fly off into the wild blue yonder and do little more than make noise, smoke, and smell.
As a result, the person holding the bang-stick is going to need to have it secure against the recoil. Pushed against the shoulder with the firer braced to absorb the recoil works fine. Resting against, say, the chin isn't such a great idea, and if this is tried, new techniques will quickly be developed.
The science dictates the basic form - long tube, mechanism to initiate combustion that can be operated with one hand, means of holding the bang-stick securely. If a design doesn't take account these (and other) factors, then the design won't work very well (if at all). But any design that meets the factors is viable. In the case of the bang-stick, the factors driving design do tend to lead in one direction, which is why the arquebus is recognisable as the same sort of thing as a Lee Enfield.