Would James Cotton's instrument be too strident for a smooth jazz band?
Let’s work this out in a step by step way to be sure we have the right answer.
yes
Smooth jazz is an offshoot of jazz music that relies on a more melodic form.

Smooth jazz employs the following instruments: saxophone.

guitar.

piano.

trumpet.

synthesizer.

electric bass.

and drums.

James Cotton was a famous blues harmonica player.

.

So, the final answer is yes