The most likely answers to this question is that they either ended up in the hands of one or more soldiers who liberated Wewelsburg Castle or that they ended up, similarly to a whole lot of other Himmler stuff properly included in the archival collection known today as "Persönlicher Stab Reichsführer SS" (Personal Staff Reichsführer SS) that can be viewed in the German Bundesarchiv and the American National Archive. If the safe as such existed at all.

The thing here is that this question is not that easy to answer because the only secondary source that includes a larger discussion of the safe and its supposedly super secret content is Karl Höffkes, Stuart Russell: Die Wewelsburg – Das weltanschauliche Zentrum der SS (The Wewelsburg – The ideological center of the SS). The reason why this presents a problem is simple: Both Höffkes as well as Russell are Holocaust deniers, well known in Neo-Nazi circles who are more interested in pro-Nazi myth making than in serious historical inquiry.

Russell, a Brit, who did a lot of consulting work for the BBC and other film documentaries about the Wewelsburg was a known supporter of HIAG (Hilfsgemeinschaft auf Gegenseitigkeit der Angehörigen der ehemaligen Waffen-SS, literally "Mutual aid association of former Waffen-SS members"), a German Waffen-SS veteran lobby organization whose main objective was to achieve legal, economic and historical rehabilitation of the Waffen-SS and who engaged in a massive propaganda effort to that effect that would often cross the line into Holocaust denialism. Specifically, their goal was to produce massive amounts of pop- and amateur-scholarship that portrayed the Waffen-SS as a "normal" fighting force, innocent of the charges brought against them and to justify their crimes. When Russell died in 2006, the HIAG Mitteilungsblatt praised his historical work and called him "dedicated to historical truth" and "one of their own", indicating his strong sympathies for a group of people dedicated to justify and deny genocide and massive crimes against humanities.

Höffkes' case is even more obvious. He has been well known as part of the Neo-Nazi scene in Germany since the 1980s and had been part of the Bund Heimattreuer Jugend and evenr an his own publishing house that, among other Neo-Nazis and Holocaust deniers, published the works of Armin Mohler and the former SS-Ahnenerbe officer Herman Wirth. In 2012 he traveled to Iran to speak at the Holocaust Denier conference organized by then Iranian president Mahmoud Ahmadinejad, which represented a novelty in the German Neo-Nazi scene because it represented the outcome of a network project of extremist shiites and Neo Nazis in Germany. He is also very good friends with David Irving.

So, what should immediately become clear here is that Russell and Höffkes are not reliable historians but rather Nazi apologetics and that therefore their writing about a secret safe of Himmler's with super secret documents is to be taken with a huge grain of salt because deniers like them have been known to make a huge hubub about allegedly super secret documents of high ranking Nazis, which they purported to somehow disproof the Holocaust (of course, nothing of the sort has ever materialized). The fact that Russell has worked as a consultant for a large number of WWII documentaries is with a high likelihood the reason why the "Wewelsburg safe" tends to come up in documentaries like this.

However, even if we assume that the safe existed for the sake of argument, the context of what we know about the Wewelsburg and the work habits of Heinrich Himmler tell us that the safe most likely didn't contain any super secret documents that would have been contained historical revelations on a grand scale.

Wewelsburg was despite its frequent portrayal in popular media as a place of mystery and the occult a place that ultimately was of secondary or even tertiary importance within the SS itself. While Himmler was a fan and had grand plans for what to do with it, the actual usage during the Third Reich was a rather limited affair and very little of Himmler's grand plans for the castle came ever to fruition (including the Coat of Arms collection or the death's head ring collection). Only one meeting of high ranking SS-officers ever took place there in June 1941 as ideological preparation for the war against the USSR and according to the transcripts no decision was made there. The rest of the time, the castle served as an SS-school for both the SS-Ahnenerbe, which also undertook archaeological excavations in the area and established a small library on early Germanic history. While Concentration Camp prisoners did undertake construction there and a small detachment of Waffen-SS troops was posted there, that was about it. It was, at most, a place of fantasy and a place where pseudo-historical research was conducted and with the war starting in 1939 Himmler barely spend any time there.

What's also important in this context, especially when it comes to the alleged content of the alleged safe, is that Himmler was a am who was known to spill a lot of ink on a lot of subjects. Peter Longerich describes him as a far from prolific but compulsive writer. This becomes clear when one surveys the content of the aforementioned archival collection "Persönlicher Stab Reichsführer SS" (Personal Staff Reichsführer SS). Next to some very relevant historical documents, it contains a truly staggering number of rather random memoranda, letters, and orders by Himmler. Among them, for example, are a 16-page treatise on how to best breed female horses (something Himmler had no experience with, having worked as a chicken farmer before joining the SS), a three page memorandum on the merits of the increase of playing dodge ball in schools (it builds character according to Himmler), a request for increased research by the SS-Ahnenerbe into the old Germanic art of building special fences in Southern Tyrol, and a wealth of correspondence between Himmler and a variety of medical researchers in the Third Reich, where Himmler – a man of no medical experience – suggested on how to improve on their research. In short, the man was very bad in holding back his ink.

Assuming a safe existed in Wewelsburg, the most likely content of it would have been his writings on the plans for Wewelsburg as a sort theological center for the Germanic SS-cult Himmler aimed to build – a project that is of very little historical significance simply because all attempts to initiate it on a grand scale were shot down in the mid-30s by Hitler himself in order to secure the support of the Christian Churches in Germany. Meaning that if it ever existed, the safe's contents would be prattle about how Himmler envisioned his new religion – a subject that has been documented and dealt with extensively over the years if not for its historical significance then for its pop-cultural shock value.

In summary: The only source for the existence of the safe is the writing of two known Holocaust deniers and should it have existed its content would be of secondary historical importance because it would consist mainly of Himmler's ramblings about his SS-cult.