IMO It’s necessary to apply noise reduction to all of it : words and gaps, then apply a gate to cut back the volume of the hiss in the gaps between words. Before writing your cheque make sure the software can actually produce a better result than Audacity, I’ve not tried Mr Davies program but I have tried trial versions of GoldWave and others, they all create artifacts when Noise Reduction is applied …
[ Steve’s noise gate here … Noise Gate - #12 by steve ]