I think some accordions are noisier than others, depending on the thickness / hardness of the felt on the flappers.

The recent "Cajun Accordion Kings and the Queen" album that can be watched on youtube is a good demonstration. Some accordions are dead silent, some clapclap a lot (all recordings are solo accordion, in the same conditions).

Personally, the clapclap never bothered me. It's a nice organic sound. Same thing for the rockers hitting the bottom of the keyboard. Nice rhythmic sound of wood hitting on wood.

There's a good chance the clapclap would be drowned in the mix too and no one would ever notice.