Quickly reducing the level during the offensive sound is about as good as you can do easily. If the the visible peaks far louder than the music are your caterwauler, you can easily reduce those to the same level as the music and make them at least less invasive, probably without introducing other obvious audible artifact. You may be able to reduce a bit further, but the reduction will become audible as the music level suddenly decreases, sounding much like a limiter cutting in (which is what it is- a manual peak limiter applied just to those instances).
With more work you can sometimes do some interesting tricks-
If mostly on one side, you can copy the opposite channel and do a quick cross-fade to two-channel mono and back. That can be less invasive than reducing signal level during the wail, since only the stereo imaging is effected and not the level of the music.
Similarly you can use Mid/Side techniques to cross-fade to more Mid-dominated mono or Side-dominated mono if the offense is in the center or the more diffuse ambience. There is a Michael Gerzon paper from 1990 about various kinds of cross-fading tricks to do this, back in the analog mixing era, by setting up routings so a single fader could be rapidly moved in real-time to more easily reduce pops, dropouts, and these kind of unwanted noises during a dub with minimal artifacts.
http://www.audiosignal.co.uk/Resources/Outside_the_mix_A4.pdfThe best modern approach to this are probably noise reduction commonly tools referred to as spectral editing tools. They allow one to draw envelopes around offending noises on a spectral display that plots frequency against time, and apply clever algorithms to partly reconstruct the cut-out frequency bits from the unaffected surrounding time/frequency material. Izotope RX is probably the most well known, can run standalone or as a VST I think, and is rather pricey. Samplitude has this capability but is an full featured audio editing program. Sony offers one I think, and I'm sure there are others, including very expensive tools from CEDAR and the like. These are fantastic tools for this kind of thing which can near magically remove coughs and other noises, but they are complex and tend to be pricy unless included in the editor's built-in tools.