Don't worry about it too much. Through your index funds you are not invested in a currency, you are invested in companies.
Whether a fund is denoted in EUR or USD does not matter at all. One share of iShares MSCI World contains 0.006 shares of Apple. More generally, any MSCI World fund consists of 1.88% Apple. Whether you consider the value of the fund in EUR or USD is irrelevant for that.
Sure, if the USD should ever completely and utterly tank, that will have serious repercussions on American companies and, therefore, your investments. However, such a black swan scenario will influence European companies, too.
Of course, it is not unlikely that there will be some significant fluctuations in the EUR/USD exchange rate that will influence the details of how your portfolio is doing. But in the long run what counts is how well the companies you are owning do. And then we come back to diversification. By investing everywhere, you are decreasing your total risk because you are making yourself less dependent on one single currency or economic region.
My own asset allocation (within the stock part of my portfolio) is roughly 40% Europe, 35% US, 25% EM (the exact numbers are pretty arbitrary in my opinion and in the long run probably irrelevant). I don't hedge currency risk at all and I am happy with that.