Suppose Nobel doesn't invent dynamite.
He doesn't become a multimillionaire and Bofors doesn't move into armaments manufacturing.
How would the world unfold with weaker explosives...and no Nobel Prizes?
What you suggest won't happen at all. There were too many people messing around with chemistry at the time and dozens of people working worldwide trying to "tame" nitrogylcerin. Nobel was just the guy who won the race, nothing more. Nobel's use of diatomaceous earth wasn't the result of some intellectual
tour de force either. Like Edison and the incandescent bulb, Nobel's breakthrough was a result of brute force trial and error.
As for the Prizes not being set up, nothing is lost there. The Prizes have been politicized from the beginning, the process has devolved almost to the level of a farce, and even the hard science prizes are more and more awarded to scientists at the end of their careers for discoveries made decades ago.
If he still invents nitroglycerin then there is a far more explosive and far less controllable explosive in warfare.
Noble didn't invent nitoglycerin.

It was first produced by an Italian who was basically a grad student studying under a French professor at a northern Italian university who was investigating gun cotton among other things. Nobel happened to be the French professor's other grad student.
The stuff scared the Italian grad student so much he kept his discovery secret for over a year and only published when it became clear others were going to publish their own results in the field.