By comparison, the loop code suggested earlier by DushiPunda was taking so long that I stopped it and measured what had taken place up to then... after 7.5 minutes, the loop had processed only 91,357 rows of the 200,000 that were there...
For those who might read this thread in the future... DushiPunda's solution will only trim outside space. If you want to apply Excel's TRIM function which does that plus it collapses multiple adjacent internal spaces down to single spaces, then you can use this macro...