Before I begin it is worth highlighting that the HRE is not a particularly Germanic institution. See the answer below by:

u/LiterallyBismarck (https://www.reddit.com/r/AskHistorians/comments/6rheh5/why_did_it_take_so_long_for_the_various_german/).

The short answer to your question is no, the independence of the Dutch did not hinder the Holy Roman Empire's naval capabilities. What hindered the HRE was its geographical location which predicated a long-running fixation with continental politics until the 19th century.

Access to organic naval capabilities would certainly help but it was hardly critical. During the 15th to 16th centuries, seafarers were relatively abundant on the European continent. Alternatives to the Dutch, to name a few, included seafarers from Italy, France and Portugal. Given the existence of the Hanseatic League with its prominent role in facilitating trade in the Baltic, it is likely Germans themselves likely had substantial naval capabilities of their own. But that is beside the point. The point is that states that did not have extensive seafaring capabilities could look to hiring foreigners from these states to lead expeditions or to develop organic naval capabilities; should the need arise. For instance, foreigners famously played a prominent role in the establishment of the Spanish Empire. The first building blocks of Spanish America were laid by Columbus, a Genoan. The expansion of the empire to Asia, by the way of the Philippines, was laid by Magellan, a Portuguese. Both men originated from polities that were not under the control of the Spanish empire at the time of their service. The example of the Spanish empire was not an isolated one either. Despite the existence of organic naval capabilities, states such as England and France too hired Italian explorers to discover new trade routes to Asia. For England, it was John Cabot or Giovanni Caboto. Cabot charted a route to North America, specifically Newfoundland in 1497-98, which helped with the establishment of subsequent new England colonies. For France, Giovanni da Verrazzano explored and charted the eastern seaboard of North America, between Newfoundland and Florida, in 1524.

So with this in mind, why should the loss of the Netherlands be crippling to the HRE's ability to create naval capabilities or overseas colonies? The Netherlands did not hold any form of monopoly on seafaring expertise in Europe. If for whatever reason, the Germans did not have access to Dutch seafaring experts, they could still hire Italian or even Portuguese experts. And if the behaviour of the Italians, Portuguese, and even the dutch themselves, were an indicator, the existence of an independent Netherlands did not mean that the naval expertise of the Netherlands were out of the reach of the HRE. If so desired, the HRE could simply employ Dutch explorers and shipbuilders like Imperial Russia. During the time of Peter the Great, Dutch shipbuilding experts were employed to develop Russian naval capabilities, creating a shipbuilding industry and a European style navy from the ground up. It is also unlikely that the Dutch would outright refuse to work for the HRE. Dutch grievances were with the Spanish branch of the Habsburgs, not the HRE. If anything, the Dutch might even be positively predisposed to working with the germanic states given their commonality in religious affiliation. After all, both the Germanic states of the HRE and the Dutch were protestants. Finally, If absolutely necessary, the HRE could simply embark on the expensive and time intensive process of trial and error, assisted by imitating others, to develop organic naval capabilities.

Thus, the creation of naval capabilities and overseas colonies were tied more to political will/needs and with the ability of the polity to fund such endeavours. In this, the Germanic states of the HRE were notably disadvantaged. The Germanic states of the HRE had neither the will nor the resources to engage in overseas adventures and were typically fixated on continental European politics. When the Spanish and the Dutch were building their Empires, the Germanic states were embroiled in the cataclysmic thirty years war. The war, which played out predominantly in German lands, was extremely brutal and substantially depopulated Central Europe. As you can imagine, as the Germanic states bore the brunt of the war, they were in no shape to fund any foreign overseas adventures even if they wanted. Thus they missed out on the first phase of European overseas expansion. Even after they recovered, German states were doomed to be fixated on continental politics given their central location in Europe. Their centrality meant that german states were often the battlegrounds of the feuding European powers. Thus, the political environment of the German states did not allow for any substantial maritime adventures as resources were often consumed by petty wars. This fixation on continental politics would not abate until the German states were able to guarantee their security. This was only achieved in the 19th century with the formation of Imperial Germany. Imperial Germany being the most dominant power was able to acquire the requisite security which was denied to the Germans for centuries. This security coupled with a burgeoning German economy provided the Germans with both the requisite political will and resources to develop substantial naval capabilities and an overseas colonial empire. This is very clear in the rapid acquisition of a colonial empire. Between 1884 to 1914, Imperial Germany acquired an extensive colonial empire that had holdings in Africa, East Asia and the Pacific. This was parallelled by the unprecedented expansion of the German Navy. During the Wilhelmine period, Germany constructed what was the second most powerful naval fleet in the world from scratch, innovating and developing technologies with very little foreign input.

I hope I have, at least, answered some of your questions. As to the question of whether the Netherlands is the epicentre of the HRE's overseas trade and potential naval operation, I do not know enough to answer that. All I know is that the Netherlands was part of the Hanseatic League which played a prominent role in Baltic trade which the northern germanic states partook heavily in.