CAD would certainly make it quicker and easier, but cams can be plotted on paper, accurately, without trial-and-error.
You need determine the high and low dwell angles, which will bound arcs struck from the shaft axis, divide the rest into closely-set but equal divisions, then put the radius on each from a graph of the “unwrapped” locus alongside the cam plot itself.
The graph angle (x-axis) scale is not important, the radial (y-axis) scale is, matching the cam’s maximum radius even if the plotting is to a large-scale. The number of angle divisions should of course be the same on both parts of the plot. The more the better, within reason.
The technique is somewhat similar to plotting a development in sheet-metal fabricating.
The slopes can be of various types: linear, harmonic, etc., depending on the requirement but what drawings you do have should give some idea. They might simply be as tangents to the two dwell arcs.
Once plotted as a set of polar co-ordinates, the cam itself can be milled using a rotary table (a DRO is great help here for setting the radial travels). The resulting, small waves or facets are blended smooth by hand, by file or vertical linisher.
(I’ve not tried it myself but that describes how I was taught to design them, and how they were made in the printing-machine factory for which I once worked. They made both axial cams, by profiling a cylinder’ length, and radial, cut from gauge-plate discs.)