Replacing caps on crossovers?

The negative aspects happen if you willy nilly replace caps that go to ground. Especially with 1980's, 1990's or earlier speakers. You alter the ESR and the impedance makes your amps work oddly.

Series caps are usually pretty safe to change.

When / if you replace coils, keep the DCR the same.

Musichead. If the speakers are working properly there is little to gain and usually you have to do some surgery to get to the x-over risking damaging other parts like the drivers. If you are not happy with your speakers use the money to save for new ones.

Swapping caps is easy. Depending on how good and carefully matched your existing caps are and how good the new cap is your results may range from disappointing to unbelievably impressive. Just no way to tell from the meager details provided.

In terms of voicing, tweaking the speakers tone or frequency response, swapping same value caps doesn't really affect this. Changing cap values changes crossover frequencies and will affect voicing. What most people want is what they already have only with less grain and glare and more refined detail. This you can usually get with higher quality caps without affecting the overall tonal balance of the speaker as long as you stay with the same value caps.