The earliest mention of unclutter
I found is dated 1922 in a novel entitled Saint Theresa written by the the American novelist, Henry Sydnor Harrison.
Talk slanted off to the general problem of the records. The expert's
plan to set up a separate "dead" file, to help unclutter the present
broken-down system, proved pleasing to the sales manager who confessed
that as the files were now, he was frequently guilty of "holding out" on them. 'T was n't right, but what was a man to do?
This predates Merriam-Webster's aforementioned claim (1930) by a number of years. I would like to know if The Oxford English Dictionary has an older citation.
Conversely, the earliest citation I found for declutter
is dated much later, 1961, in Volume 129 of Country Life
Action Against Clutter
It has been said that because only abnormal happenings make news, virtue does not qualify for the reporter's attention .... Happily, that is not an absolute truth. An
appreciable amount of publicity has been accorded to the fact that the period between June 5 and 12 was declutter week, in which a well-organised effort was [rest snipped off]
And “de-clutter”
which pre-dates my reference, Wednesday 22 November 1944, found by @Josh61
I have looked in Etymology Online and in Oxford Dictionaries Online too, neither of these authoritative references provide dates and Etymonline, surprisingly, completely ignores both terms.
This leads me to conclude that unclutter has the longer history while declutter appears to have been coined twenty years later in the United Kingdom.