There are various kinds of pulse shaping filters, but since we are dealing with sidetone, the purpose of which is to serve as feedback to the operator manipulating his/her paddle, the shape of the filter, and hence the resulting sound, should be determined solely by the aesthetic sense of each person.
This makes the problem extremely difficult in a sense, because there is no way to determine the best.
One candidate is a raised cosine shape. The shape, used in a frequency domain, is very popular in the field of digital communications, because it can limit the bandwidth of the signal without introducing Intersymbol Interference (ISI).
Does the envelope look like a raised cosine?