How would you clean the inside of your converter?

Depends on how clean you want to get it and how dirty it is before you start.

Air will blow most of it out. A brush is usually required to loosen the stubborn dirt. But even a little cleaning will help if it's real dirty.

If compressed air damages anything then it was already a bad solder joint.

If you do use a brush you need to be reasonable but something like a paint brush should be soft enough.