I recommend doing it the same way a dialogue editor would - manually edit them out, small crossfades in between. Then try a noise supression tool after the fact as icing on the cake. It's a great way to learn how to edit in practice. Take dialogue for instance. anyone editing voice must learn the intricacies of inflection, rhythm, and cadence - and furthermore, how to alter it in believable ways (hence, dialogue editors are called invisible artists - also why there's the saying "a seasoned dialogue editor is worth their weight in gold"). Unfortunately a catch-all like a plugin for this siuation won't help all that much in my opinion and you frankly won't learn a whole from it.
Pushing a plugin button is limiting, a skill limited to the confines of a certain tool and its availability. Learning to carefully and transparently edit sound however is a skill which you can carry on forever, regardless of the tool or medium, it transcends the tools, and put it to practice in many ways and constantly improve upon.