Have connected my share of air compressors . Preferred to use a fusible safety switch with quality 200KIAC rated fuses. Can not remember ever having a problem with any air compressors that shut off at 120 #'s air pressure and only using fuses no more then 150% higher then motor FLA. In some commercial garages they needed at least 135 to 140#'s of air pressure to operate air jacks to lift up loaded trailers so they did not cut off until 150 #'s . In that case had to use a time de!ay fuse rated 175% higher then motor FLA. Had trouble with a couple of jockey air compressors on sprinkler systems where they had the cut in & cut off too close together and air compressors would short cycle ( on & off several times a minute ). You should not have any problem with the existing #6 copper wire. In larger plants where they had several air compressors running at the same time we had tech install think it was an unloaded on at least one air compressor that ran entire production time. At end if day they flipped a switch to return it so air pressure switch controlled it. Had one one a 200 HP screw compressor.
Unless there’s a leak somewhere (or no air reservoir), a compressor that pressurizes a sprinkler system shouldn’t run more than once per day!