The idea of exploding your gunpowder inside of a metal tube to propel a small piece of metal at your enemy is not exactly the most obvious way to use it.
The most obvious use of gunpowder, and the one that the Chinese used for centuries, was rocketry and flame-throwers. I believe that if Europe is held back from discovering gunpowder's many uses until the 1500's or maybe the 1600's, introduced by Ottoman conquests, then gunpowder would be primarily used in proto-bombs and rockets. The Byzantines would be desperate to find a way to combat the Ottomans, and monarchs would want a fast and quick solution to defeating their nobles. If some Byzantine scholar figures out the formula behind the Ottoman's rockets and own fire-squirters, we could see copies adopted to combat them, and as it spreads across Europe, a wave of improvements to the basic designs and accuracy of the rockets instituted by Europe's many kings.
These kings would use the rocketry technology to destroy or conquer the castles of their enemies, effectively ending the age of castles just as the cannon did in our timeline. If a few substantial military victories over Ottoman fortifications were made directly prior to their adoption, and gunpowder improves the formula of Greek Fire even more to allow for a sort of flamethrower-type weapon in the West, then the idea of the bullet (or cannonball) may be slow to come.
Rockets would be cheaper than a huge casted metal tube, less dangerous to those lighting them as they fly far off before they explode, and more effective than the earliest cannons. European kings would not want cannons in this situation. The only people telling them about this absurd idea would probably be one experimenting scientist or general, or maybe a da Vinci-esque person. The cannon would be seen as the da Vinci inventions seemed to those of their contemporaries; fanciful, expensive works of genius doomed to fail in the real world. Why invest in this cannon idea when hwacha-like inventions and better rockets and even mines are being thought up that are proven to work? The treasury is only so wide. So, it seems plausible that, while guns are impossible to delay inevitably, they could be delayed until maybe even the twentieth century!
But what would a gun-less world look like in the meantime? Well, combustion engines would probably take much longer to catch on, as controlled explosions wouldn't be a proven thing. When they do come about inevitably, firearms wouldn't be far behind, but in the meantime steam engines would probably do the heavy lifting. In naval warfare, rams could stay the preferred tactic for a long time, while Greek fire-type nozzles become popular in the West and big rocket launchers could be added to the Eastern Chinese junks. At the advent of steam power, Greek fire would be nigh-useless against steel ships, and rockets would be hard-pressed to sink them, so a sort of steam ram could develop in place of cannons, a call back to the olden days.
On land, masses of pikemen and flanking, elite cavalry would still remain the most largely-used tactic, with supplementary artillery and maybe mine/mine-disposal crews added in. The artillery could take up a sort of Jannissary-type role as an elite force of only artillery users that almost control the government. A situtation like that in, say, France, would be very interesting.
Colonialism would be greatly affected. First of all, it could start off way later due to the lack of cannon on European ships keeping them from muscling into the Indian Ocean trade. This is what would lead to the gradual leaking of knowledge of Greek Fire to Western Europe, which outfits its ships with the deadly stuff and burns any opposition. However, they could not siege and take port cities, so they would be able to play the role of pirates only, not conquerors. In the Americas, their lack of guns would certainly hurt them, and they couldn't take such vast swaths of land. The Incas would probably be able to get their act together given the extra time before colonialism kicks off, though the Aztecs and friends are still doomed. They would be pushed back at first in this timeline, but they would easily win in Round Two due to the same disease epidemics that racked the New World. This could lead to some interesting Raj-like scenarios, as the Europeans would be too weak to fully control the areas they conquered. Princely native states would owe their allegiance to whichever European power got there first to help defeat their rivals in chaotic post-Aztec Mexico (after the disease, they would be doomed to collapse, they had too many enemies even on the inside.) These small city-states and clan groups would be slowly assimilated into a growing whichever-European-it-is Empire. The complication would be that, once the word of gold and riches gets out, other Europeans would want their mitts on Mexico, and even independent explorers. Mexico would become a mess of competing powers vying for control over small, factionalized warlords and city states, and the Inca would be totally fine (except for disease, of course.)
Settlement of the South American regions outside of Central America and the Inca would be slower, more deadly, and restricted to mainly just the coastlines, until mass-produced rockets are being made (industry should still pick up eventually, first in either China or England.) Argentina might be the exception, with the unifying force of the European powers chosen over the domestic enemy of the Inca trying to expand beyond the Andes. North America would be even harder to settle, and outside of the Canada area, mostly restricted to coastlines and easily navigated rivers like the Mississippi, where Greek-fire/rocket wielding ships could be sailed in (with shallower bottoms based off of old Norse designs to allow travel in river or ocean.) Places like the Iroquois Federation and the Navajo civilizations I could see easily modernizing, and maybe even a semi-feudal Cherokee state.
I'm planning writing an interactive fiction story on a site called chooseyourstory.com, and I need some help with the plausibility of this timeline in the background. The story would take place mid-to-late nineteenth century (just before the discovery of cannons, and soon after, firearms,) and I would like to have some discussion of the effects on areas like Africa, Oceania, Indonesia, and Japan, as well as civilizations/empires/society in India.
Please do not argue about the plausibility of the lack of discovery of firearms, that is the whole premise for the interactive fiction story, and it has been argued *millions* of times before on this board. Discussion on the effects of a lack of firearms would be extremely welcome, as would some more semi-plausible "Rule of Cool" stuff I could add in (even though it could be argued that this whole idea is semi-plausible "Rule of Cool."

) Just some ideas, help, and discussion please, keeping in mind that the story would be adventure/exploration themed, maybe akin to the 80 Days app, though less involved due to software limitations and my own lack of coding skills.