Let's sy Bismarck ignores the pressure of the parties and the population and doesn't support colonies because originally he hated colonies
The causes of Bismarck’s shift to support of formal colonies are debated, but generally it is thought to have been caused by both domestic and foreign affairs.
On the domestic side, the colonial societies and the merchants of Northern German port cities (Hamburg in particular) had been gaining steam and popularity. Their calls for colonial expansion could still have been ignored, but not without risk.
Additionally the colonial proposals were supported by the National Liberal party in the Reichstag. They had been allied with Bismarck until his turn to protectionism in 1879. And had lost their leading place in the Reichstag in 1881. Some of the party split off to the left but the remainder ended up allied with the Conservatives who were Bismarck’s new base of support. It seems likely that the colonial support from Bismarck was a part of the process of welding this alliance. Additionally, the support for colonies can be seen as an extension of the change to protectionism. Bismarck was effectively granting imperial protection to already existing German economic interests.
It’s also speculated that Bismarck wanted to create tension with Britain before the Anglophile Fredrick became Emperor, but that seems less likely to me.
On the foreign side of the equation the gaining of colonies was often seen as a sign of Great Power status. And thus the German acquisition of them was seen as extending the principle of balance of power over the whole world.
Bismarck didn’t support the colonies without reason, in other words. So if he doesn’t support them ITTL it’s possible it will cause him political issues. Probably not enough to sink him, but possibly enough to make his job harder.
And in any case, Bismarck will still be moved out by Wilhelm in 1890. Wilhelm wanted more direct rule, and Bismarck was an obstacle to that. After 1890, it is Wilhelm’s opinion that would matter, and it seems unlikely that he would hold back from formalizing those existing commercial interests with colonies.
Would that also mean that Germany would probably not invest in the 2nd largest navy?
Wilhelm also wanted a fleet. And he supported Tirpitz because Tirpitz could give it to him. Tirpitz actually deprioritized the colonies as a driver for the navy, shifting to building against the RN (with predictably bad results for the relationship with Britain). So little is likely to change on the naval score.
What could change things is Heligoland. The Germans had wanted Heligoland for some time. Had tried to negotiate for it several times in fact. But they had backed off to avoid distracting from other issues, and due to the reluctance of British governments to talk about it. Salisbury bringing it into the discussions on East Africa was a surprise to all parties. But the Germans jumped on the chance regardless.
Without formal imperial support for Carl Peters work in East Africa, there is no negotiation on trading the protectorate over Zanzibar for Heligoland. That means that the Germans are stuck trying to negotiate for it directly. And though the British massively undervalued the island, it was politically difficult to give it away. Salisbury faced significant criticism for it even IOTL. This is likely to be a continual point of tension between the two nations. The island is a massive problem for any German naval campaign with a hostile Britain. I could see Salisbury being open to trading it for something but I am not sure what the Germans would have to offer for it. And German diplomacy got progressively worse through the 1890’s and 1900’s. Which seems unlikely to endear the British public to giving away British territory to Germany.
