In recent scholarship, there's been a lot going on about what was called "Divine command theory" (DCT). Some of it interacts with an earlier literature about voluntarism with relation to God's will.
Recently, Robert Adams has been a major advocate of DCT whereas Mark Murphy supports a distinct view called "divine will theory." In DWT, it's God's will that determines the content of morality whereas in DCT it's God's commands that determine its contents.
In general DCT has been advocated by some Christian thinkers. C. Stephen Evans has applied Adams' account to Kierkegaard's thought. Adams is a Christian, as is Murphy. In all three, it is not necessarily the case that the commands be written in a book.
And for DWT, it's not even required that it be translated to us clearly (or perhaps at all? This of course raises its own problems).
But DCT (as distinguished from DWT) accepts the language transmission problems and makes God a type of communicator with people (Adams specifically cites Wolterstorff's Divine Discourses as reaching similar conclusions and looks at William "Bill" Alston's book on experiencing God).
All of this is just background to answer your question, I'd say there are three ways of "believing in DCT" that could involve not believing a holy book:
Direct receipt of divine commands
There's going to be an interaction between one's account of "inerrancy" / "progressive revelation" / "error" in relation to the holy book. For instance, you could believe the bible contains divine commands but not everything attribute to God is a command from God (or conversely you could hold that every thing in the bible is so). This is going to be a bit of sliding scale (with all the problems incumbent on picking and choosing passages within the text).
There are also counterfactual believers in DCT who assert that if there were a God, divine commands would be a definitive source of moral knowledge. (I'm trying to remember who advocated this but am drawing a blank).
A learned what God wanted from nature view (i.e., natural law regarding morality) would probably not qualify as a DCT on the contemporary definition due to the lack of communication. It might qualify as a DWT depending on how that all parses out (e.g., can we perceive what God intends through creation?).
Another interesting potential variant on DCT can be found in Hegel. I'll just leave this as brief addendum but in Philosophy of Right section 270, Hegel suggests that religion captures truth, and through this, it substantiates the moral state. The rub of course is that Hegel is not a theist in a traditional understanding of the term. Instead, he thinks religion is true -- because/when it captures the nature of Spirit (representationally). That seems to provide a basis for a Divine-inspiration theory that's not anything like the others: "If, then religion constitutes the foundation which embodies the ethical realm in general, and, more specifically, the nature of the state as the divine will, it is ... only a foundation; and this where the two diverge."
Adams, Robert - Finite and Infinite Goods Oxford University Press, 1999.
Alston, William P. Perceiving God (1991)
Evans, C. Stephen - 2006 book on Kierkegaard
Evans, C. Stephen - God and Moral Obligation (2013).