This one’s a good question because it’s not your typical “stay in one scale” kind of song. The chords don’t belong to one key. Verse chords are D, Gm7, C. Chords over the solo starts with D and then C, Bb repeated a few times. For simplicity with soloing (especially if on the fly) I’d consider the Gm7 and Bb to be the same thing.
In terms of scales and the need to think quickly, I would use D major pentatonic over the D chord, B major pentatonic over the Gm7 / Bb and C major pentatonic over the C. This would essentially work, possibly a few notes not sounding great but also not totally out of place.
If you have time to work with the song first, as opposed to having it thrown at you in the middle of a gig, then I’d try to be more melodic with it and find ideas more similar to the record.
Listening to the original recording you can hear typical country stock licks / phrasing over the D chord, using essentially the D major pentatonic.
Over the C and Bb is a simple melodic phrase based on C major and Bb major arpeggios / partial major scales (that’s how I hear it). If I wanted to expand on this and find new ideas to play with then that’s the idea I’d play around with to find what works.
You could try stock country / major pentatonic licks over each chord. Major pentatonic and major scales that change with each chord.
Hope that makes some kind of sense. Feel free to ask again if it doesn’t. This could make an interesting article that could run into a few pages long.