Base on your drawing it looks like you have a lcd, though I don't see any lcd code. Jsut a side note to your question.
I am not a a arduino master though I have learned a lot of the last few years of making projects using them and I am not a fire works expert. Frankly I was shocked I can buy e-fuse and other pieces off line with no questions asked. Now based on that statement I will give you some insight to save you some headache and issues later.
1: When wiring the the e-fuse to the relay make sure you wire it so it is in the off position to the button is pushed. (lesson learned), test the relay wiring with a sensor or something else to see the state of it before wiring the fuse to it.
2: Make sure your buttons have debounce statements in them as not to get confused on pushing them, vs holding them and so on. this is a common issue when using buttons and the arduino and could cause pre-mature firing. The example code you provided looks to have this functionality. Make sure if you change the code around you keep that.
- I like the idea of the N button like an abort. You could possibly add a time out too. If a option is not selected in 10 seconds then back out. I would suggest maybe adding some security to it as well so not any one can use it. For example a keycode or a electronic lock that when you insert the key closes the circuit allowing the firing button to be used with the program.
That is just my two cents. Good luck.