This is slightly difficult to answer, and you've already mentioned the main reason for why it's difficult in your question: the Dutch fleet ("Staatse vloot") wasn't a single permanent entity.

The naval defense of the Dutch Republic was in the hands of the five admiraliteiten, each who built and equipped warships. These warships of varying sizes mostly fought in naval battles in the North Sea (the Anglo-Dutch wars and the battle for Duinkerken to name a few), but weren’t particularly more numerous or stronger than their adversaries as evidenced by the many lost battles during the Anglo-Dutch wars. In other words: the “professional/standing/official” fleet of the Dutch Republic wasn’t remarkedly stronger or more numerous than other European naval powers.

Furthermore, the question is difficult to answer because it is hard, if not nigh impossible, to determine how many ships (of war) non-European powers controlled. By far the majority of surviving documents are from European sources that simply didn’t have information on non-European naval powers. It would be downright incorrect to make such claims without having the full picture.

But! You mentioned the VOC and WIC, and you could definitely argue that their ships should count towards to grand total of the Dutch naval power. Both Companies (VOC and WIC) mostly relied on heavily armed merchant ships for defending convoys and sieging cities, real naval battles didn't happen that often, sometimes even aided by fleets of local rulers^((1)) and even pirates^((2))! These merchant ships weren't necessarily converted, for they were already heavily armed (especially in comparison to non-European ships). But sometimes when fleets were formed for military actions, they would only stock necessities: trade cargo and passengers would've been replaced by extra ammunition and soldiers.^((3)) However, even if we consider all these merchant ships as part of the Dutch naval power that still wouldn't count all the untold thousands if not millions of canoes, pirogues, junks, rowboats, and other boats and ships that could've been used for warfare that existed throughout the world.

Did the VOC, WIC, and Staatse vloot combined have one of the most formidable and numerous fleets in the entire world that identified with one nation? Most definitely: the Dutch could and did during the 17th and 18th centuries project their influence throughout most shipping lanes and coastal regions between the Dutch Republic and the West-Indies and Asia. Did they own "half of the fleets of the known world"? No, that is both presumptuous and Eurocentric.

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(1) For example: during the conquest of Makassar in 1666, the Dutch were aided by rivals of the Makassar state. You can see war canoes on the right side of this picture https://www.rijksmuseum.nl/nl/zoeken/objecten?q=Speelman&p=2&ps=12&st=Objects&ii=0#/RP-P-OB-67.708,12

(2) Like during the battle of Liao Luo bay, where VOC yachts were reinforced by some 50 Chinese junks. Andrade, Tonio, ‘The Company's Chinese Pirates How the Dutch East India Company Tried to Lead a Coalition of Pirates to War against China, 1621 1662' Journal of World History, Volume 15, Number 4, (December 2004) 415-444.

(3) see for example the (disastrous) expedition against the "Angrean pirates" (navy of the Indian Maratha empire). Wetering, H.C.M. van de, ‘De VOC en de kapers van Angria. Een expeditie naar de westkust van India in 1739’, Tijdschrift voor zeegeschiedenis, Vol. 10, 2, (1991) 117-130.