Progressive noise reduction at start and end of songs

I’m used to reducing background noise throughout a track (eg constant air-con rumble or fan hiss), but for a live session in an inner-city church, with just voice and grand piano (recorded together), I’m noticing some annoying traffic rumble only at the beginning and ends of songs (but thankfully not evident during the song)

Any ideas on how to progressively ‘slide the noise reduction in’ just at these times, but have it non-active for most of the rest of the song ? I’m guessing I’ll be mostly using a suitable Wavelab 9 or 9.5 inbuilt NR (any suggestion which is best ?) or perhaps Waves X-Noise ?

It could be that some simple frequency-specific ‘shaving’ might be all that’s necessary, as the reverb tail of the last voice and piano notes die away into the church ambience…as the traffic noise become evident (perhaps only 2-4 seconds max, at the beginning and end of a song)

Thanks for any suggestions on how to accomplish this progressively, transparently and without drawing attention to the processing …in WL 9.5 !

If your songs are clips, then if you use a Noise Reduction plugin on these clips, you could use an envelope to automate the wet/dry ratio changes where you need.