I’m not sure that the modern phrase comes from this Old English compound, which only appears once in the OE corpus, and may be an innovation of the Beowulf poet. Compare it to dædhwæt, which makes five appearances in OE poetry. It’s more likely that the modern phrase was reinvented at a later date from the same constituent elements.
I also disagree with the existence of the OED’s first definition of keen as “wise, learned, clever.” The first cite under that definition is from the Old English translation of the Meters of Boethius:
Se wæs uðwita ælces þinges cene and cræftig, þæm wæs Caton nama. (He was a philosopher of all things keen and crafty, whose name was Cato.)
Given that there is no other Old English use in this sense, it is much more likely that the relevant sense is that of “bold, daring,” and selected for alliterative purposes. The early Middle English citations under this definition also seem to fit the “daring” sense (although I haven’t investigated them thoroughly), and the cite from 1400 would appear to fit under sense 4.a., “operating on the touch or taste like a sharp instrument,” which is a later development, but in place by 1400.