I think in this sense you have to not see mapping as in and of itself a direct tool of conquest, as if a map all by itself defeated non-Western states and societies. There were times that the imperative to map was a justification for a military expedition that engaged in conquest, but even there, mapping is like missionization or anti-slavery 'humanitarianism' or enforcing 'peace', an ideological pretext rather than a direct technology of conquest.

Where mapping and maps become a direct part of imperial power is after conquest, in structuring and elaborating a spatial structure of administration and authority.

In much of sub-Saharan Africa after the "Scramble" of the late 19th Century, for example, French, German, British, Belgian and Portuguese administrations famously came together in Berlin in 1885 to draw lines on the map of Africa that had never been there before. Sometimes the degree to which these territories as they settled into shape in the early 20th Century were arbitrary has been overrepresented: some of the new imperial territories corresponded roughly to implicit boundaries that were salient to existing African societies. Sometimes they were absurd or ridiculous--Gambia isolated from the rest of Senegambia, or the peculiar shape of Zambia (called Northern Rhodesia during the colonial era).

But even the territorial boundaries which made some vague local or regional sense nevertheless were different in their nature as lines on a map, enforced by modern state institutions (border controls, etc.) People who previously traded, interrelated, etc. could suddenly find themselves on two sides of a border, each of them under the control of a different European power, and thus dealing with very different administrative structures and unable to move easily back and forth. (David Gordon has an excellent article on the consequences of this at the border between Northern Rhodesia and the Belgian Congo in the International Journal of African Historical Studies, 34:2 Jan 2001). Sometimes that created new opportunities too for power over territory, or for smuggling--Paul Nugent's excellent 2002 book on the border between Ghana and Togo lays this out very well.

But those territorial boundaries were only the beginning. French and British administrative policy, with some slight variations, approach authority over Africans in roughly similar terms. (The Belgians and Germans sort of followed suit, though the Germans held their colonies for a relatively short time.) Essentially they decided that every African in their new possessions needed to be classed as belonging to a single specific "tribe" and that every "tribe" belonged to a specific demarcated territory within a given colony and thus that every individual ought to live where his "tribe" was supposed to live. This involved all sorts of impositions and erasures--people who had kin in two different linguistic, cultural or political communities weren't allowed to claim that any longer. Groups who had some degree of deliberate vagueness or flexibility about their membership and identity had European anthropologists and administrators telling them suddenly: this is who you are, this is where you belong, these are your customs, we've got it written down and mapped now and that's just the way it is.

Mapping enabled comprehensive systems of administrative control over the movement and residence of Africans. Sometimes those were extensive and punitive, and shifted or moved entire communities to relatively infertile land with the intention of making them into laborers on land controlled by white settlers. Where there were no white settlers, maps still often moved people off land they had had access to--land sold to European companies to be used for plantations, land reserved for missionaries and mission stations, land where European administrators decided that one group belonged there and the other one didn't even though many groups might have moved through or used land before.

Most African cities today struggle with the legacy of colonial maps, even now: many of those maps laid out cities where African residents were intended to be there only temporarily, as laborers, and where the residences they were grudgingly allowed to inhabit (in areas with little or no infrastructure) where laid out with vast amounts of vacant land between them and the central business district and any area where whites were intended to live (usually near the CBD). That has created almost insurmountable challenges in terms of infrastructure and transportation, among other problems. Imperial rule was profoundly spatial: race and power were inscribed into the land via a whole range of mapping instruments, in a way that has been immensely difficult to overcome since independence.

​ That's a really interesting question, I hope someone else will provide a more direct answer. The time frame you're asking about is outside my own area, still I thought to mention two of my earlier answers on mapping in the Spanish empire - hopefully of some interest. In both the main gist is how the Spanish crown aimed to collect infos and maps in order to gain better control; which then made clearer the limits of using such knowledge in early modern times:

• More directly on the collection of early geographical knowledge

• On borders in Spanish America, as background to the first answer

Of course this is very different beast from the 19th century. Still the Spanish under Philipp II were probably the first European colonial empire to collect this type of information systematically in pretty massive amounts (which glimpses I got of on archive visits impressed me).